Again, you're dead wrong as far as american intentions during the War of 1812 where concerned. Many openly spoke of annexing the Saint-Lawrence valley, Jefferson saying that the fact that the waters of the Mississipi and the Saint-Lawrence mixed in some spots was a sign of destiny that both great rivers where to be rulled by the same people being only one example among many. I have yet to see any sources advocating for an american pupet state in Canada coming from the US in that era.
The American Army actually lead three drives to Montreal, with the intent to go for Quebec afterward, during the War of 1812. Two of them pettered out quickly, sure, but that doesn't change the mindset behind them. The most serious one, in 1813, could have easily succeeded had it not been for two heavy american defeats at Chateauguay and Chrisler's Farm.
The 1813 drive to Montréal is pretty pertinent to the matter at hand too since it happened after the disastrous British defeat at the Thames, who would have allowed the americans to secure Upper Canada relatively easily had they concentrated their attention directly to it. Going for Montréal instead only make sense if you have design on Lower Canada as well.
As for american ambitions toward Canada during the American Revolution, be that as it may but that doesn't change the fact that Canada was openly spoked about as a possible 14th state and that Franklin did attempt to get the whole package, not just the future Upper Canada, during the negociations in Paris, tough he quickly understood it wasn't gonna happen.
Jefferson said many things. He also prophesied a sister Republic to the United States on the Pacific Coast called Cascadia. I don't think his words will necessarily translate into national policy. Regardless, all I'm saying is that I think that initially the Americans will probably set up a provisional government and that integrating that government into the Union is not a certainty and the Americans may decide to just leave it as a semi independent ally. And even then I'm not ruling out the possibility of a future annexation if say the fledgling Republic were to default on its debt and it asks to join the Union provided that the Federal Government assume the debt ...
As far as the War of 1812 is concerned, after the Battle of the Thames the British still held naval dominance in the Great Lakes and that made the logistics of the US invasion of Upper Canada quite difficult. The attempted invasions of Montreal were done with the intent to secure Lake Ontario.