My own "United States of the Americas and Oceania" TL is a good halfway step towards that goal. It uses PoDs somewhat similar to what you suggested.
It starts with the British Parliament passing a Quebec Act that was as oppressive to the Quebeckers as the other "Intolerable Acts" were to the 13 colonies. Given that George III had a very strong anti-Catholic bigot attitude, he still yielded a great deal of influence over the Parliament at the time, and assuming some random incident occurring between the Franco-Canadians and the colonial administration beforehand, the change is fully plausible. PO Quebeckers eagerly join the other Colonials in rebellion, and their swing makes the Patriot movement win out in Nova Scotia as well. I share the opinion that this is likely the easiest and most plausible PoD to make Canada join the US into a seamless whole.
America fights the ARW successfully with Quebec and Nova Scotia joining the 15 founding states, and gaining Bermuda and Bahamas as well. America and Britain reluctantly agree to a kind of joint ownership about Rupert's Land, even if contrasts over it linger.
The 15 states draft a Constitution much like OTL, with some tweaks (The Quebecois get a "domestic institutions" states' rights' guarantee about their language and Church, and butterflies from that make a stronger Bill of Rights that is enforceable against the States, line item veto for the POTUS, and explicit Congress' power to give economic subsidies to business, create independent agencies and exeuctive departments, acquire and manage territories).
Butterflies make the Iroquois confederation join the Patriots during the ARW (which makes the USA develop a more integrationist attitude towards "civilized" Indians) and Washington gett a third term. The latter change butterflies away the Alien and Sedition Laws, and expands the Quasi-War into a declared Franco-American War which the US win. These changes in turn usher in a 40-year Federalist political hegemony, which the party puts to good use with steadfast dedication to develop US economy, infrastructure and military rather more than OTL. The peace treaty and later Lousiana Purchase give America Hispaniola and the French Caribbean as well.
When the War of 1812 occurs with pretty much the same motivations than IOTL (only substitute Rupert's Land to settled Canada), the USA have a much better strategic position and a very efficient Army and Navy to kick the British out of mainland North America, and invade Jamaica, Hispaniola, and Guyana while the British are busy with the Napoleonic Wars (and they are also rebuilding a colonial empire in southern Latin America). In the meanwhile, America also gives strong support to Simon Bolivar and other Gran Colombian and Peruvian pro-independence fighters in the South American Wars of Independence (greater success in the ARW and the FAW has given the US a bit more manifest destiny attitude), which turns those leaders strongly pro-US.
Another independent PoD at the end of the Napoleonic Wars occurs. Britain, France, and Austria come to blows with Prussia, Russia, and Naples over the Poland-Saxony issue. While they are fighting, Napoleon stages it comeback, and turns the war into a three-way conflict. Napoleon crushes the British at Waterloo, but it is eventually swamped by Prusso-Russian numbers, Austria is steamrolled. British morale crumbles and they sign peace with America and the Prusso-Russians.
America gains Rupert's Land and Northwestern Territory (Pacific Northwest remains a joint ownership but it is ceded to America later), Jamaica, and Guyana. Gran Colombia and Peru become US protectorates, later US territories, and then states (more multicultural and integrationist US has less concerns about assimilating large numbers of Hispanics).
Britain builds up its new colonial empire in South America, which ensures long-standing imperialistic rivalry with America. All the way, it maintains a rather stronger military, economically develops and settles North America somewhat faster than OTL thanks to Federalist policies (which eventually become bipartisan) and integrationist attitude to Indians. Britain remains alienated, but dares not interfere with the development of a stronger US, having to face a strong great powers bloc in Europe of a successful Prussia (which soon unifies Greater Germany), Naples (which soon unifies Greater Italy), and Russia (which gobbles most of the Balkans).
The Mexican-American War occurs earlier and with California and Rio Grande breaking away and joining the US like Texas, but just as successful for America. It annexes northern Mexico down to Tampico and turns the rest into a protectorate.
By 1842, this is the world map (courtesy of Helios-Ra):