Ironically, we didn't need Map Making to meet 4 civs.
Both Arabia and Iroquois have popped towns. Does that make me unlucky with my hut?
1000 BC - Trade WM, CoL, Math, 34 gold from Iroquois for Polytheism. Trade 54 gold, WM from Arabia for Polytheism.
QSC stats:
7 towns (pop 14), 1 worker, 17 warriors (3 vets), 3 galleys, 2 barracks, 266 gold, 4 contacts.
Missing Philosophy, Currency, Construction and all optional techs.
149 shields collected for - perhaps - Great Lighthouse. (38 turns left.) Eventually, New York can take over the cow and speed this up.
900 BC - Met Germany. Traded contact with France and England, WM and 53 gold for scrap techs. Trade gold and world maps from England and France.
730 - War on Aztecs, using upgraded warriors and the odd horseman. Captured Tlateloco.
610 - Captured Tenochtitlan.
550 - Discovered Monarchy. Got a 4 turn anarchy, tried again but got 4 again.
510 - Gave Monarchy to India.
490 - Aztecs destroyed.
350 - Flipped palace to Tenochtitlan.
I had ended up changing my GL build in New York to Forbidden Palace.
310 - Popped a "skilled warrior."
190 - Calcutta flips, odds 0.4%-0.7%.
70 BC - India destroyed.
230 AD - Germany destroyed. Peace with Iroquois for town, Currency, gold, WM.
Enter Middle Ages. No AI has a Middle Age tech.
340 - Feudalism.
430 - England destroyed. Disasterous RNG vs France.
450 - Iroquois destroyed.
480 - Arabia destroyed.
520 - Finally got my first leader -> Great Lighthouse -> All luxuries.
New York changed from Great Lighthouse to Forbidden Palace.
560 - France gone. Conquest victory.
I was soundly beaten by Templar_X

this time. I'm not quite sure how he did it, but he's darn good.
Possible factors:
T_x had much more gold to devour. Researching feudalism may have been unnecessary on my part.
Arabia and Iroquois may not have popped towns at world's end in T_x's monstruous game. (Of course this is not enough to explain the whole gap.)
T_x may have learned to sail better than the megalosaur, who made an effort to send separate galleys to some distant places, but for the most part ended up ship-chaining to Berlin.