But the desert is not on my way to anywhere (yet). I have to cross and road a hill to get to the GL & forests anyway, so adding a mine only adds 3 extra turns. Moving to the desert tile for the sole purpose of a pickup tile would be 6 turns. My head hurts.
Your first worker should go to the floodplains, not to the grasslands & forests, so the desert would not be too far off. (An early second worker can go north later.)
However, I think for the 5-turner you don't even need to waste worker turns for a "pickup tile": if I didn't miscalculate again, it already works with just one BG.
The ingredients are: 3 irrigated floodplain (iFP), 1 mined BG (mBG), 2 mined grassland (mG), 1 forest (F).
On the first turn we move our settler 1NE in order to get that extra grassland. We chop one of the two forests, the other one is left intact. Hopefully one of the 3 grasslands will turn out to be a BG. The cycle then starts at size 5 and runs as follows:
1. 3 iFP, 1 mBG, 1 mG --> 5f, 4s
2. 3 iFP, 1 mBG, 1 mG --> 5f, 4s + 2s by picking up the F on growth
3. 2 iFP, 1 mBG, 2 mG, 1 F --> 3f, 7s
4. 2 iFP, 1 mBG, 2 mG, 1 F --> 3f, 7s
5. 3 iFP, 1 mBG, 1 mG, 1 F --> 4f, 6s + 1s by picking up a hill on growth
Total: 20f, 31s !!
However, I still believe that due to the barb situation a 6-turn warrior/settler combo might be better?!
Or even better yet: one of the two forests reveals a deer on a BG... Then all our calculations here will have been in vain and we'll just run a normal 4-turner...
BTW: I'm pretty sure that templar_x and Megalou are right, and my suggested 4-turner with one turn at size 7 is nonsense...