There's some useful posts above, but there's an elephant in the room - the American revolutionaries knew they were winning, as their decisions to turn down the various British peace offers in 1775-81 makes clear.
Ironically, if the British had been willing to offer what they did DURING the war BEFORE the war, they might have been accepted; as it was, each successive offer gave the Americans more autonomy, if not outright independence, and so indicate pretty clearly where the political, economic, and demographic trend lines were going... And so the Americans were confident enough to turn them all down.
The other issue is simply that the return on trying to hold onto Western Hemisphere territories with significant populations, especially those on the mainland(s), generally didn't pencil out for European powers in the Eighteenth and Nineteenth centuries, as witness the retreat of the British, Spanish, Portuguese, French, Russian, and even Danish colonial holdings and the collapse of the "late" attempts at European imperialism in Latin America, notably those of France and Spain in the 1860s.
It was an age of nationalism, on both sides of the Atlantic; expecting anything less from "Western" people's at this point in history is swimming against the current, so to speak.
Best,
As to the first point-Indeed, Britain was short on imagination after 1778 and Continental control of everything bar Upstate New York, New York City and Georgia was solidified, and the Latin powers forced Britain to spread herself thin on the defensive, after that its' pretty much hold out and win for the US. However, any contested territory in 1775-7 was still "Up in the air" as it were, as the frequent defections, desertions and switching sides which occurred-demonstrating that had the more fluid and imaginative warfare of 1776-77 been maintained into 1778 and 79, the eventual stalemate may have seen Britain holding more than just New York and its' environs-justifying the importance placed on Fort Constitution and West Point.
The Continental Army didn't storm New York City, and had the dawning of the stalemate seen all between the Delaware and Hudson Valley fortified like New York was-I doubt that could have been successfully stormed-drastically changing the situation
True, Thomas Paine's work changed the landscape drastically-and these offers were trying to paste over the Entire war, yet Diplomacy tends to be reached when military means are exhausted-the USA didn't gain Canada or Arcadia because they were solidly in British hands once both sides had been exhausted-had the same been the case with Georgia or New York State (Both with substantial natural barriers and local Loyalist following)
Granted, if it was militarily possible to hold a "Southern Canada" out of Georgia, the Floridas, the Five Civilized tribes and as much of South Carolina as one can garrison-it would likely become independent (If it even survived to the 1900's), and follow its' own course-yet having more Canadas in one's sphere of influence while having a smaller (And possibly split in two) USA may have achieved two things-Bigger set up for round 2 during the Revolutionary Wars in Europe, 1812 or later, and kept British attention on North America rather than adventures in India
Ah-and yet the Current cannot be mistaken for a Whig interpretation of History, for it is the Victory, and indeed the Success of the USA following the Revolutionary war that proved a knock-on effect to just about every independence movement based on Nationalism since. The dominant or victorious power sets the Current of history, Republics, Communes and Free Cities had existed long before-yet success more often than not wore a crown, the Communes of Northern Italy became the Duchy of Milan, the Dutch Republic became a Kingdom. American success inspired emulation, every attempt of France or Britain to build an Empire or hold on to colonies had to contend with America sitting there doing its' own thing being all successful
I got the idea while reading about the intense debate between the Virginian and New England factions as to the future of the USA, and how their compromise shaped the USA we know today-I wondered what would happen if the two went their separate ways, creating their own brave new worlds without half-measures. The "Southern Canada" idea I got while researching Andrew Jackson's policies on the Cherokee, and thinking of how the deep south and Virginia would be impacted by this British South, Abolitionist, Loyalist and with five substantial tribes there-It would have made for an interesting war. But I suppose for that, I would have had to have written a set-up and then posed a more limited question-what would you think?
Regarding George Washington's Fabian tactics,
in baseball terms, can we say he pitched a good game and avoided giving a meatball right down the middle?
Hah, in Football terms-his holding midfield did a damned good job and made Britain pay on the counter, But yeah-pretty much