As a possible reference/parallel/alternate look as to what Canada/US borders would have looked like in a different War of 1812 I highly recommend the TL "Dead Skunk"
It does add a sort of independent/protectorate of Louisiana but the northern bits are sensible and it's one of my favorite TLs.
It's a great timeline, but the peace between Britain and America is hugely flawed. If the British were savaging the American coast that badly and got all the way to Boston America would have given Britain almost anything to end the war right then, especially if New Orleans had fallen too.
Wellington was a great commander but he flubbed the landing in that peace.