Update: I don't think its the DME/sensor because it's not happening only when hot. Even if I kill the engine after romping on it, it will sometimes restart right away; conversely, the other day the car was cold, I accidentally started it in gear (oops) and went to start it again and no dice.
Someone suggested it may be the fuel pump relay, which I'll try first 'cause its cheap/easy. I also bought a spare FPR/fuel pump to try afterward, if necessary.