FallingStar, those are several interesting thoughts.
Back when AI War was a TBS game (for about a week, at the start of its alpha), I had devised a system of "realtime turn-based" that was more forgiving than the typical turn-based turn timers like you see in Civilization. Basically you would have Action Points that would get refreshed by some amount (say, 50) every turn. Turns would automatically end every 30 seconds, automatically adding 50 to everyone's stockpile, whether they were finished with their prior turn or not. So if I was done and had 0 AP left, I now had 50. If you'd done nothing and still had 50, you now had 100. Etc. If everyone got down to 0 AP before the 30 seconds was up, or hit End Turn, then the turn timer jumped to 0 and you'd go straight into the next turn without having to wait. And there was a cap on the amount of AP you could accumulate, something like 500, so that you couldn't stockpile it ridiculously though you could take time to think. The idea was based around a way to make a TBS game work with a better flow in multiplayer when some players are actively fighting, others are considering their options, others are doing upgrades or what have you, etc. I was real frustrated by multiplayer in Civ IV.
Anyway, something along those lines, combined with some of your ideas, could also work.
Another way to do it would be to take a page out of the D&D book, and have Minor Actions and Major Actions. The minor actions might be on a turn timer that auto-progressed in realtime every couple of minutes, while major actions work as now in the game. Kind of along the lines of your idea there. Minor actions for the player's NPCs might be things like exploring or producing goods. Minor actions for the overlords might be things like producing troops, moving the troops around, and so on. Major actions would be things like constructing buildings, attacking enemies on either side, and so on.
So if you leave the strategic side of things for a really long time, this would mean you might find yourself under an awful siege that you then have to break. But you'd never find your town preemptively burned to the ground. There would still be a lot of complexities to then address, but it's interesting at least.