OK, I have something of a Vinland-survives-sketch.
In 1001, Erik the Red brings his company of 160 men to L'Anse Aux Meadows and settles there. The early days of the colony are precarious and marked by conflict with the Beothuk, but by 1030 or so a dozen or so villages, comprising about 1500-2000 people, dot the Newfoundland coast. The Norse mainly live on fishing and cattle-raising. By 1100 the Norse colonies, including a largish minority of Beothuk-Norse creoles, are about as big as Iceland population-wise and have started to expand to Prince Edward Island and Nova Scotia, which are warmer and allow agriculture (mainly rye and some wheat).
At this stage, the impact on North America is small and the impact on Europe virtually nil. Some contact with Norway and Denmark is maintained, but since expeditions are expensive and the Vinlanders don't really have much to pay in the way of tribute, it's sporadic. The government, so far as there is one, consists of a "governor" at L'Anse Aux Meadows with no real power, appointed by Copenhagen, and the smaller singr (parliaments etc.) of the individual villages.
It probably isn't until 1300 or so that the situation starts to bear any fruit: the last Greenlanders, faced with a cooling climate and pressure from the Inuit, migrate to Vinland, and the expeditions from Denmark become even more infrequent. About 150,000-200,000 Vinlanders and creoles occupy Newfoundland, PEI, and Nova Scotia; smaller Norse settlements are found as far away as Cape Cod and Montréal. In the absence of a central government, Newfoundland, PEI and Nova Scotia have founded the Ausing, a central parliament and court. It doesn't (and can't) do much other than settle disputes between villages and occasionally send small expeditionary forces against hostile Native Americans, and even those have limited scope. The ethnic situation is becoming much fuzzier, as European grains and cattle raising have spread among the Native Americans. (Smallpox may not be an issue. It wasn't introduced to Iceland until 1241, and may never have hit Vinland at all; and of course cowpox confers some sort of immunity).
I have to get going, but I'll continue this train of thought...