both agree and disagree. overall, you're on the right track, but...
OTL, Britain didn't really think much of the US as any sort of power. they were surprised that the US, despite its early bumbles, rebounded to be halfway decent. TTL, Britain mostly has its way, or does better enough to allow for Britain to get its way at the peace table. Presumably, the war winds down in a similar timeframe, or quicker (Britain, as shown OTL isn't going to extend it to get better terms, and the POD states that Britain comes out ahead). While you are correct that Britain wanted that trade restored, it'll happen either as OTL, or in TTL. Trade has a tendency to follow the money trail, and that will remain with Britain. And, US, having lost 3 cities and the (greater than OTL) economic destruction associated with losing a war, will be far more desperate to restore trade. So, you'll have a victorious Britain deciding what it wants and doesn't want. US can whine, but if, per you, it wants NYC, Baltimore, and New Orleans (three major and vital cities) back, along with trade restoration, US will gladly give up far more than periphery territory. a decade of settlement in Louisiana territory still leaves it as mostly periphery. Control of NO is control of Louisiana.
The hogtie of US was meant as a reason for Britain to take more of the continent. OTL, the main reason British/Canadian footprint isn't bigger is because Britain correctly saw that US trade was worth more than a flag on the ground/color of a map. If we're going to make the footprint bigger, we need a reason. I put that reason as recognition of US potentially having ambition, and hence looking to limit their expansion at a propitious moment.