I think I might have seen that map at the Map Exhibit at the Field Museum. There were so many maps, though, that I might be mistaken.
That reminds me of the map of North America at the start of the alt-history SF novel "The Two Georges" by Richard Dreyfuss (yeah, that guy) and Harry Turtledove (prolific alt-history author). The book proposes that the US lost (or didn't fight? I forget) the revolutionary war, and the title refers to a paining of George III and George Washington signing a peace treaty or somesuch.
I particularly recall there was a large Souix (or other tribe) Indian province below the Great Lakes.
The large Indian province south of the Great Lakes would make sense. The British had a non-expansion policy when it was just the 13 colonies.
I learned in Georgia history class (required in middle school) that before the Louisana purchase the colonies/states didn't know how far west the continent went, so Georgia passed a law that its western border ended at the Pacific Ocean.