Sounds to me like your losing prime as it sits. You say that you replaced the fuel pump. Was this the Lift pump or injector pump and replaced it with what pump.

I had this same issue when I was still using the stock lift pump. Had it towed to a Cummins shop and they found a bad ground in the lift pump. This was allowing fuel to run back into the tank when you shut the truck off and wouldn't let it re-start because the lines were completely drained.

lift pump and just a stock one, i got all the connections at the pump perfect upon install heat shrink and all... was it the ground on the vehicle side or pump side on yours?