Thanks for looking that up, Dave. It's a bit of a bummer techs are so costly at immortal/epic! And the fact we don't start with either myst or mining doesn't help either...
Anyway I did some extensive calculations, hopefully it's worth slightly more than a one way ticket to the litter bin.
First off, "my" proposal of building SH with stone hooked up. I noticed in this case it's better to start off with 2 WBs, otherwise the worker would end up with idle turns.
T1-11 build WB, working the stone tile, 44h. Start with mysticism (or mining, same results).
T12 switch to 2f1h to finish WB.
T13 WB up, start other WB. Work the clams for 4f3c.
IBT myst comes in after 12 turns 9c, 1 turn 12c.
T21 grow to 2, after t1 of 2f and 8 turns 4f. Work stone as second tile, 8h invested now in WB.
T25 mining in after 10 turns 12cpt. Start masonry.
T31 WB2 finishes. Hook up other clam and work it. 15 cpt now. Few turns in warrior, waiting for growth to size 3.
T34 growth to 3, start worker. 8 excess food/hammer -> 12 turns. 15 cpt.
T39 masonry in. Don't know how big the discount is, may come in slightly earlier. Start wheel.
T46 worker finished, setup quarry. Continue warrior build. Work 2 clam and 2f1h tile. 6 excess food.
T51 wheel in. Start BW or even sailing.
T52 quarry up (6 turns, is it?), road it.
T53 grow to size 4. work 2 clam, quarried stone (5h?), 1f2h tile.
T55 Start stonehenge. Must be 180 hammers on epic (factor 1.5), 90 with stone. Have 8 hpt now.
T67 finish SH.
T71 BW in. Therefore maybe even better to go sailing first to start immediately on trading post after SH. Although settler comes to mind as well...
The stonemining proposal works out as follows.
T1-12 same, though researching mining.
T13 start worker.
IBT start BW, due in 25 (292/12)
T31 worker in, start WB.
T39 growth to size 2. work clam and mined stone. BW just in.
T46 workboat in. 14 food saved. start SH.
T56 grow to size 3. 60h now invested in SH.
By this time theoretically we may have chopped all 5 forests and if it would be 24h per forest, SH would come in now. Don't think that's a good idea because it leaves us without any forest to chop for TGLH at all, which we all agree is the main thing. So let's suppose 3 forests for 72h. Then we're at 132, and still need 48h. We may have a mine now, so there are 9hpt, so 6 turns more and it finishes at T62. It maybe a bit sooner even if we chop into the 2nd workboat.
So indeed the stonemining thing beats the quarry by at least 5 turns. However, the downsides are that we spent 3 forests that could have gone to TP/TGLH and, moreover, we're smaller in size and pull less commerce.
So maybe we can do the stonemining thing going WB/WB/worker to overcome this last thing.
So then till T46 it's the same as the quarry proposal. The mine may be in slightly sooner than the quarry, but I think it's obvious that this won't work out, since SH would be started with serious hammers on T50 and needing 180 hammers from that point, both other schemes work out better.
The whole thing also boils down to how quick stonehenge is generally built on immortal and maybe even if we want it in the first place.
After all this, I'm a bit undecided still about what is best. Not having enough forests to chop for TGLH does worry me though with the stonemining option. And if we lose SH in the quarry option at least the invested hammers give double gold.
And now start shooting holes into my reasoning!
Sorry for the extensive post by the way.
EDIT: In the quarry option after building the quarry we would of course build a mine on the other hill, so that shaves a turn or even 2 off of SH. So less difference.
EDIT2: Of course I may be off by a turn here or there, but generally it must be something like what I said. I think.