Basically as pointed out above, the US had a poor history with access to the mouth of the Mississippi, and the Spanish did repeatedly close the mouth of the river off, which is going to prompt the US to go out of the way to get access to New Orleans - and the longer and larger the Midwestern States grow, the larger the calls will become.
Absent a French Revolution, i doubt there'd be much in the way of British annexation of Louisiana - They can settle the remainder of BNA through the provinces in Canada, as they have control of the St. Lawrence and access to the Lakes; they don't need access to the Mississippi to shore up that support. And as the French Regime will stil lbe in such dire straits, I feel that the British will be distracted propping it up and helping the French stamp out revolutionaries... for a price.
I'd expect an earlier Adam-Onis treaty of sorts come to pass between the US and Spain. They need access to the Gulf, and specifically New Orleans. Louisiana is a peripheral territory for the Spanish as well, and its population is still tiny, with only two towns of any notable size, along with a few small settlements, that were not receiving any major settlement and not producing any major revenue for the Spanish - well, outside of New Orleans.
So, I believe a deal would be reached, with borders more favoring the Spanish (look at the red -o- line on
this map to see an approximate indicator of a potential border). the US would get most of Louisiana, with definable borders. They may or may not purchase access to the Oregon Country; it depends on the time of purchase. Heck, they may not, but come back a decade later to negotiate access to the Pacific as well.
That sounds to me like the most reasonable expectation - the US needs New Orleans to allow its hinterland unfettered access, sans New Orleans the Louisiana Interior is hard to access, and all that needs to be done is to have a price agreed upon.
The only thing is that the US would have to pay for Florida as well - the US received Florida in exchange for dropping claims to the Rio Grande Boundary that it received as part of the Louisiana purchase.