Sorry, I played before I read T-Hawk's latest comments, BUT I came to all the same conclusions he did. What do they say? Great minds think alike?
Goal 1:

the Olmecs
Goal 2: Figure out Monarchy question.
IT-
Potonchan (the Olmec capital) is located 3 tiles southeast of where our army currently is positioned, but it is on the other side of a river. Were the stack positioned one tile to the southwest, it could then move one tile south here, then I could declare war and move one tile east, and likely be in position to attack without crossing the river. As is, we'll lose one turn, but no big deal. Just something to think about in the future.
The stack moves one tile southeast. I adjust Texcoco to grow in 2 turns instead of 3, while still building the barracks in 4 turns (11 shields remain: 4 in the next two turns plus 2 on growth, then 4 on turn 3, and built on turn 4 with some waste, but already at size 3. Tlatelolco needs one more shield to be at 7spt, an archer every 3rd turn rather than every 4th. We will have a monopoly on Ritual Sacrifice, unless the AI develops it in the next 5 turns.
660Ad (1): Troop positioning. We are already 5 troops over the limit. Capturing another town or two will really help our economy.
670AD (2): Tenoch and Tlatelolco build archers and continue training them. Olmecs refuse to give Enslavement to us, so I declare war. Trailing archer captures exposed Olmec worker who heads toward Texcoco. 5 archers move on Potonchan with another a step behind. The sixth archer in the original stack sits tight to march on Chilapa when reinforcements arrive. Potonchan has a regular spear on top. It turns out that Texcoco's 5th shield is corrupt, but the barracks is still due in 2 turns, now with no waste.
680AD (3):
Attack on Potonchan:
Elite Archer d. Reg Spear 4-1
Vet Archer d. Reg Spear 3-1 and promotes
Elite Archer d. Reg Spear 1-3
Potonchan falls. [W-L: 3-0]
One Toltec archer is in range to attack next turn and also a settler/archer pair. Potonchan is garrisoned with 2 healthy archers and a healthy spear, although they are not fortified. Tlatelolco's growth requires luxuries to be raised to 30%. It now makes 7spt.
IT- Reg Spear d. Reg Archer 1-3 and promotes. Resistance ends in Potonchan. 2 more Olmec Archer/Settler pairs come into view along with the 3rd one from last turn. [4-0]
690AD (4): Texcoco's 4th shield is now uncorrupt.

Not sure why this happened. It has 2 happy citizens and 1 unhappy, so it can't be WLTKD. Anyone know why?
Vet Archer d. Reg Archer 2-3 and promotes (2 slaves captured).
Elite 4/5 Archer d. Reg Archer 3-3 (2 slaves captured).
Elite protected by 2 vet archers. [6-0]
700AD (5): Ritual Sacrifice is finished at a monopoly, but no SGL. Tlatelolco builds archer and starts Settler. I think we have enough Archers to deal with the Toltecs by now and it's time to expand. Tenochtitlan switches to granary so we can start to pump out settlers and workers. We should be able to grab 5 luxury resources when all is said and done. I trade Ritual Sacrifice to the Toltecs for Enslavement and 85 gold and to the Maya for 147 gold.
The Monarchy Question
100% science = 29 beakers = 34 turns = 986 beakers
90% science = 27 beakers = 36 turns = 972 beakers
30 beakers (using a scientist) = 32 turns = 960 beakers
55 beakers (all scientists) = 18 turns = 990 beakers
52 beakers (all scientists minus 1) = 19 turns = 988 turns
So the lowest cost I can guess is 960 beakers for Monarchy, which will decrease as it is discovered by the AI. But here's the catch (tm). At this moment, the highest research rate we can sustain is 70%, due to a required luxury rate of 30%, having moved a MP from Tenochtitlan to Tlatelolco. That is 20 beakers per turn. Within 5-10 turns we can have 2 luxuries hooked up, which could lower our luxury tax to 0 and raise our science income to as high as 25-30. Building settlers and workers will be essential in the next 40 turns since we want to fill in "our" land. This will significantly reduce our science income as population is shifted from improved tiles to unimproved tiles. Perhaps more importantly, we will lose our ability to buy other techs with gpt or with straight cash, since any perturn spending will drop the rate back to 40 turns and then all our research spending would have been wasted.
My final verdict. It is certainly possible to get Monarchy in less than 40 turns, but I consider it a gambit and I don't think it's worth the risk. We will not get Monarchy at a monopoly, so we will fall far behind in tech, and will not be able to buy our way out with terrible tech prices on Sid.
So I opt for Monarchy at 10%. Judge me lightly.
710AD (6): Chilapa is now size 2, and even though the troops are not all in position yet, I start the attack a turn early, hoping to take the city before it can whip another spear (and make it so we destroy rather than capture.
Attack on Chilapa
Vet Archer d. Reg Spear 2-3
Vet Archer d. Reg Spear 1-3 and promotes.
Chilapa falls (and is wholly corrupt). [8-0]
720AD (7): Jade is now hooked up and luxuries drop to 20%. Maya have discovered stone carving. Potonchan now requires a scientist to be content, for two turns until it is connected to Tenochtitlan by road, so science is turned off. Troops move toward Izapa. Texcoco switches to Temple (due next turn), to bring in more 2-food-tiles and hopefully border expansion will grab the spices between Texcoco and Potonchan.
730AD (8): Contact made with the Moche tribe, who have 3 cities in addition to their capital. I trade them Pottery for 60 gold. They are rather backward.
Elite 3/5 Archer d. Reg Warrior 3-2
Elite Archer d. Reg Archer 3-0
[10-0]
740AD (9): Troops are now in position to attack Izapa.
750AD (10): Tenochtitlat Granary => Settler. Road is complete between Tenochtitlan and Potonchan, so the scientist is fired and science is back to 10%. Toltecs have Stone Carving and also have 2 Maya workers and 2 Toltec workers available. They must be at war with the Maya, which means the Toltecs will be gone soon. Troops are in position to attack Izapa right now, with 4 Elite (2 fully healthy) and 2 Veteran Archers.
Conclusion- The question is whether or not to finish off the Olmecs rather than let them stay alive in OCC glory. As long as they are more backward than us they will raise tech costs for us. I would like to discuss this as a team to figure out if they are worth keeping around. Is the AI-AI trading rate sufficiently high enough on the Sid level that they could pick up a couple techs from our other rivals which we could trade for? Thoughts? I have left the army with movement until after this decision. Whatever the decision, we should send the troops to block the chokepoint as soon as possible. The name of the game now is EXPAND EXPAND EXPAND and improve our lands so we can face the Maya. Good luck to Coffee.
PS- The Spear being built in Texcoco is meant to go to Tenochtitlan. No need to keep any cities empty to entice our rivals.
RBC4d