"...It seems to me that after the car sits a while and cools off, the fuel flows back into the fuel tank..."

It could very well be. The fuel pump check valve is a likely culprit to be allowing the fuel to drain back down.

"...It also seems kind of gutless on hills, and bucks when the air conditioning pump kicks on..."

"...I've read that these symptoms could point to an in tank pre-pump..."

Resoldering the fuel pump relay wouldn't be a bad idea, just to eliminate that possibility. However, it sounds as like the pump itself may be on the way out. Your car only has one pump, which is in the tank. Some Regina owners have reported bad luck with those pumps, but I don't know that they're any worse than the rest. If you could rig a pressure guage to the system that could be monitored while driving (uphill with the A/C on and your foot buried in the throttle) it might bring the problem to light.