Why not bump a thread? I cannot speak for the initial 49th parallel really, but only for its extension into the Oregon Country. The positions of the British and Americans never really changed; the former wanted the Columbia as the border, and the latter wanted the 49th parallel. As has been recounted on this
forum, at one point the British suggested a detached portion of the Olympic Peninsula become American to offset fears of a lack of naval ports. During another set of negotiations, the border of the Columbia unofficially was offered by the United States but went nowhere diplomatically speaking. Outside of these blips, the standard response for renewals of negotiations by Americans was the 49th parallel. At least, Upshur, Webster and later Calhoun were voices of it in the 1840s.
This brings us to the 54'40 or Fight, such a popular AH bit.

Only a few men in Congress were avid supporters of the concept, namely Lewis Cass and his clique. Maybe I'm just no trying hard enough but I've only been able to find three additional men named in the group. Interestingly, or not, the "All-Oregon" lobby was the majority (or entirety) of the equally fringe but still popular with many on AH.com, "All-Mexico" camp. I'm certainly not a wizard at American Presidencies but I have thumbed through a few biographies on Polk about his support of 54'40. They generally state the position was used purely to drum up support for his election. Additionally some substantiate fairly convincingly that Polk touted the measure to finally make the British acquiesce to the long offered 49th parallel.
The British had the preeminent economic force among European descendants in the Pacific Northwest through the Hudson's Bay Company. Something once held as valid in scholarship was that the American settlers of the Willamette Valley and surrounding areas that arrived in the 1840s "saved" Oregon for America. The position became abandoned once it became clear how little the settlers and their "Provisional Government" factored into the thinking of American and British diplomats. Ironically a recent book "French Canadians, Furs, and Indigenous Women in the Making of the Pacific" spins this logic on its head by stating French-Canadians/Métis kept British Columbia, well, British.
There would need to be major butterflies to have happen, after the previous portion of the America-BNA border being set at the 49th parallel. Something like a British Republic forming during the French Revolution, or just being royally wrecked from those wars. For the Americans to go to war over Oregon, an episode would have to be engineered like OTL's Mexican-American war. Additionally, Lewis Cass would have to be President with a united backing in Congress to support his measures. For the British side of an alternative border, something fairly bad would have to occur to the United States to remove it from being an active participant [insert civil war]. Even if what is now Washington state was to settled by British, they would be like the OTL American pioneers, insignificant for the diplomatic exchanges.
tl;dr Either the United States or the United Kingdom have to be thrashed and heavily lose interest in PNW after the first treaty established the 49th parallel for an alt Oregon Treaty (and border) to become plausible.