Assuming we do go for Medicine... these are the techs and beakers left (before discount... so divide by 1.2 for base cost and remove some from trades)
^^Few wonders and Caste Artists to pop borders. Without Oracle, Pyramids is the only arguable wonder that can speed up Education ASAP... TGL ends up being a detour.
HAs will upgrade to cuirassiers, so any hammers invested into HAs will be invested in Cuirassier builds once Gunpowder completes.
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Regarding game finish: I would prefer to get the Taj early as well (not only for the bug, but for the fact that my estimates are usually conservative and 120+10+13+12 = 155; we can always spend a few turns at one point outside GA without too much loss)
GPs:
3 for last GA
1 for Corporation (GM?)
extra GMs/GSs for trade missions/bulbs
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5~7
We get Economics one for free so 4~6
900~1200 gpp.
I'm eating a bite but will think about it this evening.
If...
Lib>Medicine
44k beakers ->
36,700b base
With consecutive GAs, Oxford empire growth, Rep, Mercantilism, GM trade missions, bulbs ... I expect 1,000 beakers per turn average should be possible and so
around 40 turns is reasonable.
Lib>Democracy
46.8k beakers ->
39,000b base
Using the same premise as above, maybe a few extra turns...
say 42 turns.
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What we need: assuming we can maintain gpt expenses at around -250/turn, then we need around 10,000 gold total, or an extra 7,400.
2 trade missions = 3,000+: need 4,400, we're really not so far anymore given city captures AND I am not even considering trades for Machinery/Engineering etc.
40 turns should be upper boundary given we can get some trades in...
a great finish date would be ~T150 as I was saying earlier in the thread.
The good thing with Sushi as target Corporation is that we don't need to take as many cities so we're not limited by military conquest, only beakers.
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Graph referred to by Doshin.
By the way, getting some map trades would be nice and also revealing the last few unknown tiles in the south for strategic placement of resources.