Some submissions are still missing, but I decided to post my turnset now as well. For those who didn't submit yet: don't read... 
T031, 2510 BC:
Worker is finished and moves to the plains 2SW. I would have liked to improve the river grassland first, but this takes to long: after pondering the situation for quite a while, I found that the fastest way to get into the 4-turn cycle, is to build a worker in 3 now, then a settler in 6 and then 4-turn settlers from that on. For this I need to have 5 fully improved tiles in 9 turns from now, and the sixth tile on turn 11. The only way to have these tiles in time, is to irrigate two more plains. At the same time, that plains tile allows the next settler reaching the cow one turn faster, another advantage compared to the river grass tile.
Following PaperBeetle's idea, I switch the BG to scientist for this turn, which allows me to set lux down to 0%, so that Entremont is making 13bpt now.
Alesia is founded and works on a river BG for 2s and 3b, starts on a warrior.
Scouting warrior 1SW on the hill.
T032, 2470 BC:
Worker starts a road, warrior 1W on the inland hill. Chinese borders are spotted.
In order to grow in the remaining two turns, the scientist is sent back to work on the BG, lux raised to 10%.
T033, 2430 BC:
Irrigation finishes, worker 1 starts road. Warrior 1W.
There are 17b left on Writing, I'm currently making 13b, so I lower the science slider to 60%, which results in 9b.
T034, 2390 BC:
Worker 3 finishes and starts mining the BG.
Warrior 1W and Shift-D establishes contact with the Chinese. They are up Warrior Code and Iron Working. We have nothing of interest to them.
In order to have the necessary 4spt for a settler in 6, Entremont is set as follows:
As Alesia would have overrun of 1 food anyway, I temporarily switch it from the river BG to the gold hill. This nets the remaining 8b for Writing at 60% science.
T035, 2350 BC:
Writing finished and Code of Laws started.
Worker 2 finishes road and starts irrigation. A barb warrior appears in the vicinity, so I'll need to send a warrior for protection next turn. Luckily the road from Alesia to Entremont will be done by then.
Warrior 1S. After I met the Chinese, let's get back to the coast again.
Of course, Alesia is switched back to the BG in order to finish growth in 3.
If I wanted to, I could probably get Wheel, Warrior Code, Iron Working and Mysticism from my three contacts now, but giving away Writing at this early point would jeopardize the Republic slingshot, so I'm holding it back for now.
T036, 2310 BC:
Warrior in Alesia finishes. Luckily the barb moved away again, so I can fortify the new warrior in Alesia for now. Worker 1 finishes the road and moves to the BG 1NW of Entremont in order to speed up the mine there.
Entremont has grown to 5 and picked up the forest. I switch that back to river grassland to keep 5fpt. 4spt is enough for the settler to finish in 4. Now luxury needs to be increased to 20%.
Warrior 1S, reaches the coast.
T037, 2270 BC:
Warrior 1W.
T038, 2230 BC:
The mine on the BG finishes. I send one worker to the plains S-SW of Entremont, as the irrigation there needs to be done in 4 turns from now (current settler still needs 2 turns, and 2 more turns Entremont will be at size 5, so doesn't need the extra plains yet. The other worker is sent to the floodplain NE of Alesia. I was thinking about what would be better, first mining Alesia's BGs or irrigating the floodplains. I decided for the floodplains, because of the following reasons:
Entremont has grown to 6 now, picking up another forest. I switch it to the remaining river grassland and increase lux tax to 30%. Alesia has grown to 2. At first I thought, it would be good again to use the gold hill now for one turn to get the extra commerce, but then I realized: if I use +3 food now, I can grow one turn earlier: the irrigation on the floodplain will finish in 4 turns from now, so with 4 x 3f + 2 x 4f = 20f Alesia can grow in 6 instead of 7 turns. That one extra gold (one is lost to corruption and another one goes into lux tax anyway...) is not worth delaying growth by one turn. See the two screen-shots, Alesia without and with the gold hill:
I also wake the warrior in Alesia and send it to Entremont, moving another warrior from Entremont to protect the worker currently irrigating 2 SW of Entremont. Because meanwhile two warriors appeared on our borders, and I'm not sure, what they are up to:
Warrior S.
T039, 2190 BC:
The irrigation on the plains finished, neither the Chinese nor the Romans attacked. Good.
The worker on the plains S-SW now starts irrigating. That irrigation will finish in the interturn after Entremont has grown to size 6, so Entremont can already use the food in that interturn and the irrigation doesn't need to be sped up. Therefore I can sent the worker now to the river grassland SE of Entremont. I want to replace the irrigated plains with mined river grasslands asap, in order to get the extra commerce. The two plains can in the long run be used by the cow town and by another town on the western coast (or perhaps by a temporary town on the gold hill?!).
The other two workers (plains and floodplains) now start irrigation.
Warrior S.
T040, 2150 BC:
Entremont finishes the settler (unfortunately wasting 3s) and drops back to size 5. Alesia finishes another warrior, which gets fortified in town. Consequently I can now drop lux tax to 20% again.
The worker starts a road SE of Entremont.
The warrior that has been camping outside last turn, is now sent into the forest 1W-2S of Entremont, in order to check, whether the coast is clear for the settler to follow. No danger to be seen, so the settler follows suit.
Warrior S. Spots a furs resource, but that is so far away, it will probably not make a difference in this game.
Entremont is now setup at 5fpt and 6spt and is therefore at the start of a perfect 4-turn settler factory. The last remaining 2f/1s tile for usage at size 6 (the plains at S-SW) will be ready in three more turns, just in time after Entremont has grown to size 6.
So in turn 40, the 4-turner starts operation, which is 11 turns later as in PaperBeetle's and templar's examples. This shows that their approach (basically farmer gambit combined with an early worker before the granary) is more powerful in terms of expansion. However, as I already built a settler "out of order", I'm only "one and a half" towns/settlers behind at the moment, and as already discussed earlier, I got something as compensation for the slower start: more security, a better view of the territory and more commerce: at this point I have already collected 53 beakers towards Code of Laws, compared to PaperBeetle, who just finished Writing this turn.
It will be interesting to follow, when the "break-even point" will be reached: before or after the slingshot.

T031, 2510 BC:
Worker is finished and moves to the plains 2SW. I would have liked to improve the river grassland first, but this takes to long: after pondering the situation for quite a while, I found that the fastest way to get into the 4-turn cycle, is to build a worker in 3 now, then a settler in 6 and then 4-turn settlers from that on. For this I need to have 5 fully improved tiles in 9 turns from now, and the sixth tile on turn 11. The only way to have these tiles in time, is to irrigate two more plains. At the same time, that plains tile allows the next settler reaching the cow one turn faster, another advantage compared to the river grass tile.
Following PaperBeetle's idea, I switch the BG to scientist for this turn, which allows me to set lux down to 0%, so that Entremont is making 13bpt now.
Alesia is founded and works on a river BG for 2s and 3b, starts on a warrior.
Scouting warrior 1SW on the hill.
T032, 2470 BC:
Worker starts a road, warrior 1W on the inland hill. Chinese borders are spotted.
In order to grow in the remaining two turns, the scientist is sent back to work on the BG, lux raised to 10%.
T033, 2430 BC:
Irrigation finishes, worker 1 starts road. Warrior 1W.
There are 17b left on Writing, I'm currently making 13b, so I lower the science slider to 60%, which results in 9b.
T034, 2390 BC:
Worker 3 finishes and starts mining the BG.
Warrior 1W and Shift-D establishes contact with the Chinese. They are up Warrior Code and Iron Working. We have nothing of interest to them.
In order to have the necessary 4spt for a settler in 6, Entremont is set as follows:
As Alesia would have overrun of 1 food anyway, I temporarily switch it from the river BG to the gold hill. This nets the remaining 8b for Writing at 60% science.
T035, 2350 BC:
Writing finished and Code of Laws started.
Worker 2 finishes road and starts irrigation. A barb warrior appears in the vicinity, so I'll need to send a warrior for protection next turn. Luckily the road from Alesia to Entremont will be done by then.
Warrior 1S. After I met the Chinese, let's get back to the coast again.
Of course, Alesia is switched back to the BG in order to finish growth in 3.
If I wanted to, I could probably get Wheel, Warrior Code, Iron Working and Mysticism from my three contacts now, but giving away Writing at this early point would jeopardize the Republic slingshot, so I'm holding it back for now.
T036, 2310 BC:
Warrior in Alesia finishes. Luckily the barb moved away again, so I can fortify the new warrior in Alesia for now. Worker 1 finishes the road and moves to the BG 1NW of Entremont in order to speed up the mine there.
Entremont has grown to 5 and picked up the forest. I switch that back to river grassland to keep 5fpt. 4spt is enough for the settler to finish in 4. Now luxury needs to be increased to 20%.
Warrior 1S, reaches the coast.
T037, 2270 BC:
Warrior 1W.

T038, 2230 BC:
The mine on the BG finishes. I send one worker to the plains S-SW of Entremont, as the irrigation there needs to be done in 4 turns from now (current settler still needs 2 turns, and 2 more turns Entremont will be at size 5, so doesn't need the extra plains yet. The other worker is sent to the floodplain NE of Alesia. I was thinking about what would be better, first mining Alesia's BGs or irrigating the floodplains. I decided for the floodplains, because of the following reasons:
- Entremont will need to run at size 5-6 for quite some time now, which means lux tax between 20-30%. So in order to not waste the lux tax in Alesia, it should grow to 5-6 quickly as well.
- The irrigation will be faster than the mines.
- Perhaps I can pop-rush 20 shields into Alesia's granary. Usually I'm not a fan of pop-rushing, because in my opinion it is nearly never worth the lost population and the extra unhappiness. But perhaps in this case it can be used with benefit. (Most probably it won't, though...)
- I can reach the floodplain without wasting a worker turn, something that is not possible with the BGs.
Entremont has grown to 6 now, picking up another forest. I switch it to the remaining river grassland and increase lux tax to 30%. Alesia has grown to 2. At first I thought, it would be good again to use the gold hill now for one turn to get the extra commerce, but then I realized: if I use +3 food now, I can grow one turn earlier: the irrigation on the floodplain will finish in 4 turns from now, so with 4 x 3f + 2 x 4f = 20f Alesia can grow in 6 instead of 7 turns. That one extra gold (one is lost to corruption and another one goes into lux tax anyway...) is not worth delaying growth by one turn. See the two screen-shots, Alesia without and with the gold hill:
I also wake the warrior in Alesia and send it to Entremont, moving another warrior from Entremont to protect the worker currently irrigating 2 SW of Entremont. Because meanwhile two warriors appeared on our borders, and I'm not sure, what they are up to:
Warrior S.
T039, 2190 BC:
The irrigation on the plains finished, neither the Chinese nor the Romans attacked. Good.
The worker on the plains S-SW now starts irrigating. That irrigation will finish in the interturn after Entremont has grown to size 6, so Entremont can already use the food in that interturn and the irrigation doesn't need to be sped up. Therefore I can sent the worker now to the river grassland SE of Entremont. I want to replace the irrigated plains with mined river grasslands asap, in order to get the extra commerce. The two plains can in the long run be used by the cow town and by another town on the western coast (or perhaps by a temporary town on the gold hill?!).
The other two workers (plains and floodplains) now start irrigation.
Warrior S.
T040, 2150 BC:
Entremont finishes the settler (unfortunately wasting 3s) and drops back to size 5. Alesia finishes another warrior, which gets fortified in town. Consequently I can now drop lux tax to 20% again.
The worker starts a road SE of Entremont.
The warrior that has been camping outside last turn, is now sent into the forest 1W-2S of Entremont, in order to check, whether the coast is clear for the settler to follow. No danger to be seen, so the settler follows suit.
Warrior S. Spots a furs resource, but that is so far away, it will probably not make a difference in this game.
Entremont is now setup at 5fpt and 6spt and is therefore at the start of a perfect 4-turn settler factory. The last remaining 2f/1s tile for usage at size 6 (the plains at S-SW) will be ready in three more turns, just in time after Entremont has grown to size 6.
So in turn 40, the 4-turner starts operation, which is 11 turns later as in PaperBeetle's and templar's examples. This shows that their approach (basically farmer gambit combined with an early worker before the granary) is more powerful in terms of expansion. However, as I already built a settler "out of order", I'm only "one and a half" towns/settlers behind at the moment, and as already discussed earlier, I got something as compensation for the slower start: more security, a better view of the territory and more commerce: at this point I have already collected 53 beakers towards Code of Laws, compared to PaperBeetle, who just finished Writing this turn.
It will be interesting to follow, when the "break-even point" will be reached: before or after the slingshot.