So, OP, you mean south along the Cascades, I presume, to the Columbia River?
Or, instead, the southern boundary of the Nooksack Watershed?
Not sure what the big hubub is. In both of the scenarios proposed by OP, the British would be
gaining land, as the border would turn south into what is today Washington.
They purchased the claims from Spain in 1819, in the Adams-Onis Treaty. That's why joint occupation was established by the British and the Americans of all the Oregon Country, as both nations had conflicting claims that neither wanted to give up, and neither nation had effective control over more than a fort or two. The US signed a treaty with Russia delineating their northern boundary of their claim as the 54 40 in 1824.
Part of the reason that the Us managed to claim so much, though, was because their rates of settlement outnumbered the British rates by a large margin. The Hudson Bay Company was, particularly, hesitant to encourage settlers as it would hamper the fur trade and similar endevours, and as such British settlement only began to pick up years after the Americans, and in smaller numbers.
It's why the British claim line constantly shrank. Initially it was the 42, but then shrank to the Columbia River. It even eventually reached a point where they suggested ceding the majority of the Olympic Peninsula to the US, in an effort to keep the Columbia River.
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@joeyanonymous
I find the concept unlikely. If the mountain claim, as you showed, was taken, it'd be far easier to go with the Columbia River as the border, seeing as that was already the British claim and there is not much of a difference between the two. Doing this denies the US a port on the Puget Sound in general which, given conditions similar to OTL, seems unlikely. The British lost the settlement race in OTL. If you change it, that'd work out fine with the British going further south, but it depends on what you're planning to have happen.
And if the British win the race, then you would need to show how the Americans were stymied compared to OTL, or how the British manage to overcome the Hudson Bay Company, which was highly opposed to settlement, as it was.
For the second case, the border difference is much more marginal. Though, at the same time, I honeslty don't see the point. This complicates the border, which was drawn on a straight line of latitude so as to make surveying easy. Delineating watersheds is quite difficult, and as such this border invites fuzzy borders and potential border disputes, which the Oregon Treaty was attempting to diffuse.
Basically, there's no particular reason that anyone would be opposed to this, save for the fact that no one really gets anything out of it and the reasons to not do it are numerous, while the reasons to do it seem to only be one (pretty borders).