Perhaps some scenario where the Americans attempt another War of 1812 which goes horribly wrong for them? Maybe, say, they attempt to invade Newfoundland using mainly Quebecois militia, only to realise after declaring war that the Quebecois, being very Francophile, aren't interested in participating in American politics, having joined the Union primarily to take advantage of the chance to be ruled by a weaker government, and thus one more likely to give them full autonomy. The Americans press on with a totally understrength attack while raising more troops, their assault is quickly repulsed and the British have the time they need to move more troops to defeat the follow-up, a la RL except being in a stronger defensive position when the real American invasion starts. The US force is annihilated from the start, never has the chance to burn down York (Toronto) and the British push down and recreate the burning of Philadelphia. With fewer Americans in their path, part of the OTL force splits off to join an earlier assault on New Orleans. The city falls earlier and a peace treaty sees the Americans agree to cede the Louisiana purchase in exchange for being let off much lighter than they could otherwise have been punished. The British use the Louisiana territory largely to form their Indian Reserves, allowing native tribes to retreat to much more spacious homelands when disinherited by the USA, in a more idyllic (from the British perspective) enacting of the First Nations principle - they had, after all, wanted to prevent American expansion westwards in order to protect the natives' rights to own and control large tracts of land as their rightful homeland.
Just a quick idea off the top of my head. Of course, your scenario does make the Hudson's Bay Company's existence tenuous at best. It would be very easy for the USA to cut off its supply lines and essentially economically strangle it into vacating the territory, if they can't trade eastwards...