I wouldn't expect a reconstruction at all, unless the Brits help the North end slavery. Unless the military academies are all in the North now (they won't be because the South wouldn't stand for it), the South will have a better officer corps in an early ACW, but the North will lack the industry and manpower to compensate.
I'm not entirely sure about that. To be clear, I
was indeed imagining a scenario where Britain would be backing Hamilton. Yet we're talkin about 1920, and in a TL where Hamilton has been in charge for the past two decades. I have argued elsewhere that the whole 'American monarchy' thing is most likely to happen in a scenario where the need for a strong and stable executive is seen as pressing. I am assuming, therefore, that the monarch will have quite a lot of power, and that the federal government in general will be quite powerful. Washington himself tended to listen to Hamilton on several key issues in OTL, which I also expect to be the case here. And then when Hamilton takes over, he'll be pushing his OTL plocity plans, which involve fostering (northern) industry.
After two decades of that, I'm fairly sure the situation will no longer align with OTL. Of course, we must ask: will the southern states be able to block any of his policies via Congress? That depends on the way the 'mood' of the country evolves. If the whole monarchy starts off with a desire for a strong executive, and is succesful, then the whole 'state sovereignty' position may be far less popular than in OTL. This is a world without a Virginia dynasty, after all. Also, if
I were Hamilton - and assuming I have enough executive power to pull this off in this ATL - I would carve the Northwest Territory into as many states as possible, and (financially) encourage their settlement by people from the Northeast. That would be a nice trick for king Hamilton to get a considerable Northern majority in Congress early on, thus royally (pun intended) screwing over Southern interests.