IMO the simplest and most realistic way to reconcile "democracies don't invade each other" and "the US might do invasions now" is that the US is not a democracy within this model.
It certainly still is in a technical sense that is sometimes useful. But by other metrics, like "can the president start an unpopular war with a steadfast former ally" uhhhhh. If the military refuses an elected president's order to invade is it still a democracy?
Yes, because the military can't follow an illegal order, which is what a declaration of war without the approval of Congress would be. The military also can't spend money Congress hasn't authorized, even if the president tells them to.
Congress hasn't actually declared a war since World War 2. The President sends troops wherever he likes, whenever he likes, for whatever purpose he likes and Congress rubber-stamps their approval after the fact, and they call it something other than a war.
You're correct that the military can't follow illegal orders, but what you're describing as an example of an illegal order is just the way the US military industrial complex works.
I don't think this argument is landing that strongly.
When the people want a king, what's written in the rule book doesn't matter anymore.
https://www.theguardian.com/notesandqueries/query/0,,-3134,0...
When was it ever?