Alright, I started a new game last night and successfully founded a religion prior to turn 86 (I think like turn 83 or so?) which allowed me to enhance with a free great prophet on t86. I went Tradition and detoured to Kunas in order to found that quickly but unfortunately couldn't get to mathematics before turn 72- I think I hit it on turn 75 or so, close but no cigar and that was even with a Barringer Crater in my 2nd city. In order to hit mathematics prior to t72 I probably needed a free tech ruin.
Tech order was wheel, pottery, mining, AH, construction, calender, military theory, mathematics. Capital went shrine, monument, council, warrior, worker then settlers/workers for 3 more cities. Secondary cities went either shrine or council first depending on which was needed more to hit my targets. Considering I didn't hit t72 mathematics the councils should have been skipped but I couldn't know on turns 30-45 that I would miss t72 by just a few turns
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Missing out on the t72 free great person means no free engineer to nab Hanging Gardens. However, founding on t83, enhancing on t86, and then reforming on t120 or so has really given me a leg up in the religion game. I went Asceticism (food/follower) and Mandirs, Ceremonial Burial (faith/culture when expending GPs), Iconography (great person points, no policy wonder requirement, great person rate during golden ages), and glory of god (buy any great person with faith, yields when great people are born).
I've already spawned a bunch of great people. I think 3 engineers (grabbed Hagia Sophia and Sankore), an artist, writer, 4 great prophets total, 2 scientists, and 2 merchants. Each one has bonuses with ceremonial burial and glory of god.
I think the biggest danger in this strategy is right before you've got mathematics and haven't built much of a military. After mathematics you can knock out a bunch of Atlatists and easily hold off invasion but prior to that you probably just have a few warriors and maybe a couple horsemen if you have horses in your territory. I didn't get DoW'd but felt comfortable even if I had been by my neighbor Egypt with pretty good defensive city placement. I think Egypt wanted to DoW but waited too long and once I pumped out Atlatists he turned his sights on Austria and attacked her instead.
I'll update later with how this game goes.