I apologize for the lack of screenshots, but Civ 4 is barely at the limits of playability on my makeshift video card, and flipping over to Paint Shop Pro is painful.
Mission: Sushi
First order of business is indeed to make peace with Elizabeth. If I somehow found myself in this spot in a solo cultural game, I would make peace immediately. London doesn't have any wonders, so won't contribute anything to our empire except more maintenance costs. Before peace, I do pillage with any units with available movement, especially the stack at Canterbury. Liz's only available peace concession is 4 gpt.
Unfortunately, we've got difficulty in the brokerage department. Liz is up to Cautious as Timmy projected, but won't trade because she thinks we're her worst enemy! We're at 0 relations, but she's at +3 or better with everyone else!
So now I've got to pull 11k beakers out of our nether regions by the end of my turnset. Granada resumes its long-delayed Globe Theater. Hermitage in Toledo. Complete Madrid's mostly-done Grocer, then start a Bank, since it'll be running merchants. Most non-Legendary core cities go to Wealth, though the English cities start or continue on courthouses. I find spots to complete our ninth Jewish temple and eighth and ninth Buddhist temples. I disband a handful of ancient units (axemen, spears) to get unit costs under control.
The Great General settles in Granada, because that's the Oxford city. This is the best move for cultural victory - he'll make 2 culture with Sistine and 9 beakers with Representation. Cancel Dyes import from Suleiman since we have our own now, and sell him the cow for cash instead. Also sell Sugar to Hatty for cash. Since I'm not actually researching Biology yet, keep research off for the moment and accumulate cash.
In the trading dept, I do as Timmy says and trade with Zara first, Mil Trad to get Sci Method.
Turn 1: Great, the brokerage is there: I can flip Sci Meth to Roosevelt for Constitution. I need Const now in order to open up Corporation from Suleiman.
Turn 2: YES, Timmy's analysis was spot on: Suleiman gives us Corporation for Mil Trad. This was a SPLENDID analyis - I wouldn't have realized that Corporation trading required a Friendly rival.
Also Liz will now trade too! She gives Chemistry for Mil Trad! That's all four legs of the brokerage! OK, the research way is clear to Medicine, just need to pull oodles of economy out of my butt now. Now I can start research on Biology, due in 10 turns at -257/turn. I've got 1180 in the bank so can get halfway there at 100%.
I also sell Mil Trad to Hatty for her 400 gold. She's far into WFYABTA and isn't going Friendly, so we won't be getting anything else out of her for it.
Turn 5: At long last I can change civics! Representation is immediately necessary. Free Speech obvomgwtfbbqftw. Pacifism because I need to pop two GPs fast for Golden Age and Sushi. Caste is not immediately necessary(*). Mercantilism vs Free Market is a very close call - we've got the Representation synergy and I need GPs, but Free Market is just too strong so I take it. So it's a four-way change to Rep/Free Speech/Pacifism/FM.
(*) Caste System is not immediately necessary. I have a few things still to whip with Slavery, and I can run enough specialists in Granada (5 artists with Globe Theater now) and Madrid without it (4 Merchants is the most I can do, else it will spawn a GP before Granada does.)
This launches me from -262 gold/+526 beakers to -268 gold/+800 beakers (!) Nearly doubles our net economy!
Turn 6: Granada is set for 5 artists, 1 engineer, and 1 priest, at -5 food deficit (it won't starve doing so.) It'll spawn me a GP in three turns (my turn 9) for a Golden Age as long as we don't hit 20% Scientist odds.
Nice - someone sent a Hindu missionary to Madrid. That's a fourth religion if we want it, though we'll need Org Rel to build either Christian or Hindu missionaries.
Roosevelt comes asking to restart our Defensive Pact. Like mostly-harmless, I say sure, why not. A turn later, Suleiman comes asking for the same! I say yes to him too - this kind of military bloc should deter any and all sneak attacks. I also realize to cancel our Corn import from Wang Kon (we conquered our own at Nottingham), and sell him the clams for cash instead.
Granada has finished Globe and Toledo Hermitage, and both start on their second cathedral.
Turn 9: Granada spawns a Great Prophet, who pairs up with the Scientist kindly left over from the dominators to start the 2-man
Golden Age. What does this do to our economy? Actually not as much as I might've thought, only an extra 100 beakers, but that could well still mean the difference between sushi and tripe.
Turn 10: Biology has completed. Wow, we can get 3-for-1 brokerage value out of it: Roosevelt is still not WFYABTA and trades us Rep Parts for it, and friendly Suleiman even trades us DEMOCRACY for it. Enjoy, space team.
Research set to Medicine, due in, at 60% research at break-even... 8 turns! I'm going to make it! Everything hinges on the Great Merchant Lottery in Madrid now. I need a halftime break for some dinner now, but stay tuned...