Some more thoughts on the development of "American" Quebec postwar.
ISTM Quebec Libre will resemble the US in one respect: it will ultimately be a conservative "revolution", dominated by men of property. But there will be significant differences. On one hand, there will be no remote equivalent to the civil war with Loyalists that helped radicalize postwar American politics. On the other, as noted upthread, Quebec in 1775 had almost no tradition of republican government, and was still dominated by traditional colonial elites -- basically, the big seigneurial landowners and the Church plus a few merchants (the latter, by 1775, mostly Scottish). OTL the seigneurial class went into rapid decline after around 1800 and was pretty much gone within a generation or two, but TTL that hasn't happened yet.
So I think we end up with a Quebec that's nominally republican, but actually somewhat less free and egalitarian than OTL.
There are economic incentives for this, too. OTL, Quebec was subsidized heavily by the French, then somewhat less heavily by the British; it was a money-loser for both crowns for a long time. The key problem was that, other than furs, there wasn't a lot Quebec could produce that was economical for export. (And by the 1780s, the fur market was starting to get iffy; the easy sources had been cleaned out, and the Hudson's Bay people were coming online.) The long dogleg up the St. Lawrence, and the fact that the province was closed to commerce half the year, meant that trading there had crappy margins. British tried to encourage wheat exports; OTL, by the early 1770s these were starting to take off, but the war killed them and they never really recovered.
This, BTW, accounts for much of the legendary hedonism of traditional Quebecois culture. In the American colonies, surplus was brought to market and exported. In Quebec, it was consumed in riotous good living. One interesting side effect: while the Canadian standard of living was quite low compared to the American, the Quebecois themselves were the strongest, healthiest people on the continent. The Americans had more and better stuff, but the Quebecois ate more fat and protein and didn't get sick as much.
Anyway: The new regime will want to export -- will need to; they'll hit a specie crisis almost at once -- but in what bottoms? I think they'll have to give licensed monopolies to local merchants. There are other options, but that would be the most obvious to the 18th century mind.
Note one big difference between Quebec and any other part of North America: such a monopoly could be enforced. The American colonies had three thousand miles of coastline, making it impossible for any government -- British, state or federal -- to block smuggling. The whole Royal Navy could not enforce the excise laws. But a single fort on the lower St. Lawrence could control the whole commerce of Quebec.
So, in addition to being authoritarian, I think *Quebec begins to rapidly develop a class of rent-seeking merchants and monopolists without a close equivalent OTL. Without a close equivalent; but note that iOTL, the seignurage system had been growing slowly more oppressive for a couple of generations before the conquest, and for another generation after, as population density increased and land values rose. OTL this was slowed by the Quebec Act and then thrown into reverse by the reforms of the 1790s. After which the seigneurial class went into a fairly rapid decline... but anyway: TTL there's no British governor to reign in the arrogance of the local elites. So ISTM this is a plausible intensification of an existing OTL trend.
So: by 1787 we have a stable Quebecois government, nominally republican, but in reality run by a few big landowners, a handful of monopoly-holding merchants, and the Church. There may be a single man-on-a-horse Governor, or things may be run by a committee -- sorry, un conseil -- but anyway, it's rather authoritarian and, to be a bit anachronistic, dirigiste.
The franchise is very limited. Literacy rates are low. Total population is something over 150,000, but there are only two towns of any size, Quebec City and Montreal. Otherwise, it's a nation of small yeoman farmers. There's a bit of mining, and some iron working, but nothing resembling the complex mix of trades that made up, say, New England's shipbuilding industry.
In some ways, it looks more like a Latin American republic (albeit a very cold one, and with unusually broad distribution of land) than a British North American colony.
Doug M.