Just a random idea I've been playing with. With any POD after 1776, have the USA obtain part of, but not all of, the area constituting the Louisiana Purchase. Try to get the two halves as equally divided as possible, or at least so that it isn't a 99/1 split. Bonus if the other half is annexed by Canada. Do it however you feel fit.
Have America do badly in the War of 1812 and actually lose territory. The only territory it could really lose is Northern Maine and large parts, but not all of the Old North West. Then have America piss off Britain further, somehow, and have them dispute the Louisiana purchase in the peace process.
Britain, for whatever reason, decides to run off with parts of the Northern Louisiana purchase, Maine, and the Western half of the Old North West.
These territories on the Great Lakes are still people with white settlers, which spurs the creation of some kind of Canadian unity quite a bit faster since America will probably be less friendly and the British North American colonies themselves more populous.
This new Canada analogue then annexes later on the other British holdings north of the United States.