I've had this idea recently.
The Vikings, after discovering America, decide to make long-term settlements in the 11th century. Nothing too big, just small coastal fishing and lumbering villages to supply Greenland and Iceland. They provide themselves with cash by selling furs to the European market.
During the medieval renaissance of the 13th century which sees the first occasion reminiscent of an economic boom since the age of Charlemagne, demand for these curious and alien furs increases and eventually gets monopolized by the Hanseatic states who, like good aggressive merchant republics, go after their source and gradually force themselves into America and begin establishing trade posts and plantations, settled by the heretics and dissenters of the time (German and Dutch "republicans" and French and Italian cathars).
I think eventually it could be made into a fun RP starting after the Black Death, provided it is discussed how this early and decentralized colonization would go and its effects on the Europe of the time. It would certainly give an edge to christians over muslims, as up to this point Europe was dependent on the muslim world to connect to "world trade", while they way they could establish their own economic hinterland, and provide themselves with sources of cash crops (provided we count furs as a cash crop, but it's a loose term anyway).
And in general i find this a fun scenario.