That's a tough one...This could be a bunch of different things. Trying to give ideas without the parts-cannon approach!
Wiggling the ignition switch would be the easiest way to make sure that isn't the problem. I know it sounds silly, but you don't let the key switch "snap" back after cranking, do you? ...Witnessed it before and gotta ask.
Best guess from me would say check your fuel pressure next, if that's good it might be the oil pressure switch or positive power related. I had both of these problems before, but I don't want to lead you on a wild goose chase.
@kenh : Yours almost sounds ignition related or power related? Spitballin' here...I've heard defective ignition modules getting hot sometimes zap out while cruising down the road. You guys got the tough problems!
I also had a bad fusible link once on a Vortec truck. If the computer loses power for a second, it stalls and all the dash lights come on. Restarts like nothing happened.
Tried to keep it short unless you want more details. Hope you guys figure it out!