I really don't wish to be rude, but these conditions existed OTL, yet no serious attempt at purchasing B.C. was made. Unless you can find some sound materials on the population of Americans in the B.C., I can't begin to buy this. You are completely ignoring the UK's use of the entrenched Hudson's Bay Company to colonise B.C. Most importantly, this is acting on the assumption that the British, after spending several decades of slowly developing interest in the Pacific Coast, would just sell it for the lulz.
This is your rodeo, but I can't help but question your reasoning. None of the above is meant to discourage creating a TL, constructive criticism is an integral part of good AH. I fully recommend the classic tome The Hudson's Bay Company as an Imperial Factor by John Galbraith for a more relevant understanding of what factors and interests were ongoing in the Pacific Northwest, in case, the period after the Oregon Treaty.