I did a game like that a couple months ago.
Great Lighthouse + Astronomy rush, then proceed on colonizing all of the American coast. Cities should pay for themselves as you found them, and become really juicy once you chop a tribunal. You might want to transfer your capital to the new continent to diminish colonial maintenance later on when you expand deeper into American land. Then proceed on conquering the Old Continent once your huge empire's production kicks in.
hmm, an interesting topic, I believe mad scientist actually did this as King George in his Next generation RPC's, and TMIT did a lets play on this with Bismark (it was on a terra map, but basically the same thing your talking about). Maybe you should check those out.
Ormur said:Played an Earth game as England on monarch with no civilizations in the Americas and it's absurdly easy. I settled Scandinavia, took Paris and built the GLH. I libbed communism before I had chance to build the forbidden palace on the east coast of North America (even though I had a great engineer ready). I've almost finished settling the coastline and the first AI's have just recently teched astro, they're a whole era behind. I even managed to get a few cities in Morocco, South Africa and Australia.