Bombardment only occurs at the end of a fall turn, if over a city in spring, it's just passing through. Since supply center counting occurs only after fall turns, you can't consider Spring turn support of units.
I like the idea that allows ALL players to build after a certain bogey is met by the leader, makes sense too, once technology is available, it rapidly spreads to all others. One possible idea? The spread of technology sometimes takes a bit of time, maybe have a built in delay? if you add a delay, maybe make it available after say 30% and have maybe 2 years until available to all (or until a player also reaches the 30% mark sooner themselves) or keep it the way you suggest, I'm just thinking out loud!
The only possible disagreement I might have is the 5 space rule, that seems really far to me. Four sounds better to me, AND I would consider not allowing any spaces on the other side of an Ocean or Desert to be reachable. That makes sense as well, if you can travel 4 or 5 spaces, it's based on distance, an Ocean is HUGE, I would allow entry into the ocean but nothing past it (unless of course it is in range of a city by means of a different "path")
again, thinking out loud again