Alrighty, now I'm home. Pretty good memory for the most part. Wasn't sure about the Pentagon timing, but I did bring that one in as well with an MGL.
Your middle ages culture builds, courtesy of CivAssist 2:
490 BC: Colosseum
190 BC: Great Library
90 BC: Cathedral (I was having cash flow issues)
310 AD: Sistine Chapel
390 AD: Heroic Epic
440 AD: University (still having cash flow issues)
670 AD: JS Bach's
840 AD: Shakespeare's Theatre
850 AD: The Pentagon (MGL rush)
990 AD: Newton's University
I entered the industrial ages in 1030 AD, with Copernicus' Observatory under construction. My 1010 AD CivAssist 2 file shows the capital at 7569 culture, and 97 cpt. Of what's left, the Epic, University, and Sistine Chapel will have some useful double-culture time left. I will be finished before Bach's doubles, I think.
Research went pretty well; traded for Engineering (Russia), Feudalism (Great Library--Germany/France; Germany hit MA and got Feudalism about 2 turns before I got Education, so I shut off research until they could trade), Invention (Maya, as part of a peace deal) and Chivalry and Gunpowder (France) whilst moseying through the top of the tech tree.
Had three more towns flip to me, from three different civs: Seattle, Munich, and Coriyaxsomethingorother (Inca). The Incan town had the nearby horse source, which I didn't otherwise have; the other two were full cities when they flipped.
I actually built a culture wonder outside the capital; Tlaxcala took Knights Templar. It beat having someone else get it, and it actually sort of helped a little, kinda. It's not like I was lacking for culture builds.
The Maya met their full demise in 730 AD. The Inca followed 5 turns later, in one of the shortest wars on record (20 years). The Mongols provided war happiness in 470 AD by sneak-attacking with an archer; we're still at war with them and will be for the rest of the game.
The only bad thing for me planning-wise was building the Epic before the University. This was a completely understandable move--they're the same culture, and I could rush the University with cash--but after the army win in 380 AD, with 1 turn left on either one, I took the Epic. My second leader came in in 420 AD; it could have rushed the Epic and saved a couple of turns. I doubt it'll matter much though.