Man, no turns today.
Anyway I used your sandbox and did a runthrough with the golden age astronomy plan.
* Golden age t73-78.
* GP from Titan t74.
* GP from Ganymede t76.
* GP from Callisto AND Io t77.
Each GP produced (except the last) is being raced by cities behind it in the settling order. This is how Io manages to catch up at the end, it's producing 87gpp/turn and the costs are only rising by 67gpp.
In my case I got an engineer (from Gany) and three scientists, which means bulbing Machinery-Optics-Astro t78. But if we're missing one of these GP because it's the wrong kind, we'll only be delayed a turn as our research running all those scientists (and in a golden age) is pretty high and we can get a bunch of overflow from Compass. (If we only have two scientists, we research Optics. Missing the engineer means we research Machinery.)
Amusingly, this results in possibly the shortest time ever (since before BTS) from building Stonehenge to obsoleting it.
At this point our research slows down a LOT, because we'll want to switch back to slavery from caste and convert food into production for a while instead of into tech (so presumably also OR from Pacifism). I imagine we'll want Theology and Civil Service in short order, letting us build Maces, farm everywhere, construct the AP, and run Bureau and perhaps Theocracy. If someone else beats us to Theo though we might just skip it.
In my run, I mostly optimized for great people. I didn't make a settler for the 5-tile island.
I also screwed up some other stuff. We will be way short on hinduism spreads / missionaries by the end of it, so I suggest we make as many as possible beforehand. (Like 2-3, one for Callisto and one for each island.)
One other option to consider is grabbing Liberalism instead. The problem is I can't think of anything to Lib that's better than Astro. (And Lib itself is utterly useless except as a prereq for Communism, and State Property isn't mandatory this game.) I guess the best would be if we get an Engineer from Io as our second GP, and build Mausoleum with it instead of starting a golden age. Then start a golden age with the next one, Lib for Nationalismm, and build Taj Mahal. But all those are basically fluff techs. With the astro path we'll be able to REX across the ocean and/or beat the crap out of someone (and potentially choke others, too) and defend ourselves easily. We'll have forges started, and all the techs we really need for a while, meaning we can focus hard on growth and production. We'll quite plausibly be able to set up AP and other religious wonders and have a really solid empire that no one else can match.
Edit: Earlier I'd guessed that we would be research-constrained on Astro, but it actually matched up quite nicely. Research went up more than I'd predicted (I had guessed it would almost double) because I forgot we'd be running almost 200bpt worth of scientists.