A slightly more clear result than the historical one seems to be the most likely outcome featuring a real British victory. Occupying all the rather extensive territory you mention seems rather difficult. I would also take into account the chance that those colonial upstarts will be smarting for a rematch, maybe pretty soon, intended to take all of that back.
The problem was the same as in the 1775 war, US was too primitive, power too distributed, there is no central important place, no vital center.