I'm pretty sure our opponents think they can chop SH too.
You're absolutely right. Frankly, given the fact that 4 opponents are starting the game with Mysticism, I'd say we are in for 3 races right off the bat (SH, Meditation, Polytheism), and we can only win 1 of them.
Race to Stonehenge - The team that gets Stonehenge will have to beeline it, by settling and immediately starting it, or go Worker, then Stonehenge, and use the Worker to Chop it. Stonehenge is 60

on Normal speed IIRC so thats 3 chops (20

each). Our fast worker does that in 9 turns flat. The other teams all take 12 turns minimum, because they lose 1 turn everytime they enter a forest.
A worker is 60

. Its essentially 45

for EXP civs with the 25% discount. Generally you can work a 2

tile that gives you a worker in 10 turns. Capital 1

, 2

+ plains forest 1

2

=6 prodution/turn. 60/6= 10 turns(So if we are EXP we get the worker in 8 turns). So we would get SH on turn 19 (turn 17 if we are EXP) going the Worker-->SH route...
EXCEPT, that we need Bronze Working to use chops

. BW is 120

. You get 8

from the palace which running 100%

gives 8

per turn. So that's 15 turns to BW if we beeline it, which we can do, because India starts with Mining
So that means we get SH on turn 24 going Worker-->SH chop. So at a glance it seems EXP does not help us here, as getting the Worker faster only means the worker sits waiting longer for BW to finish. We could add 15 hammers to SH by just working the Capital 1

+ 2

forest, waiting for BW for 5 turns but that does not save a chop as chops are 20 hammers, not 15. If we are EXP though, it does save a Chop as those extra 2 turns mean 6 more

, so now we only need 2 Chops instead of three, which means 3 less turns of worker action. So 15 turns to BW + 6 turns chopping = SH on turn 21 with EXP.
The last option is to just build SH right out of the gate working our highest

tile. Assuming that's a 2

forest, we take 20 turns to SH. However, that is the same for everyone. So if anyone is before us in the imbedded order (like if they are Player 1 and we are Player 2), they will win the race by default if we finish on the same turn. If we are IND, our 3

/turn becomes 4, and SH finishes in 15 turns. We can also pick up that extra hammer by settling on a plains hill, which gives +1

to the capital. Of course if we dont spawn on a plains hill we will have to lose 1 turn minimum moving to one. Also, if we do spawn on a plains hill it is highly likely that everyone is spawning on plains hills, because some would call it unfair otherwise.
Civforum could still pick an IND leader (Capac for instance

) and since they have Inca as their civ, they start with Mysticism. If they pick IND, and go SH right out of the gate, no one can beat them to it, period. Now to me, picking IND, just so we can get SH is dumb. We could just pick CRE and then we already basically have SH. and we can go for a religion instead. But IND is good for other wonders besides SH of course.
Bottom line is that the best way to get SH is build it right away, and Fast Workers, BW, Chops, and EXP are irrelevant. The only way to guarantee SH is to pick an IND leader and build it right away. If we are not going to do either of these then we should forget about SH cause we're not getting it, maybe go for a religion instead. If we are, then I would recommend we don't pick Capac, pick someone else and see what Civforum.de does. If they pick Capac or any IND leader, then we forget about SH. If they don't pick Capac, we see where we are in the playing order. If we are in front of the other Mysticism teams, then we are a shoe in to get it and we should build it right away.
Of course if we go with CRE then we can ignore SH no matter what anyone else does.