The pressure damper from what I was reading is supposed to basically even out the pulsing pressure from the pump. In theory if it the diaphram was broken or leaking you could have an issue with surging or bogging, but your truck runs fine once started right?
Some thoughts: Even though the previous owner said a new pump was put in with the new tank, you have no way of knowing what brand or model was actually used, if in fact they were replaced. I suspect there may be something going on either with the pump or the filter sock. I think at this point the best thing to do would be stick a fuel pressure gauge on the system and watch the starting pressure and check leak down. It's possible having the rail open and all pressure relieved for a while helped the pump hold pressure when restarted, especially if its a little weak. Also possible there is something in the tank, sock, or line that is blocking the flow until it is moved with enough gas. I did find a piece of plastic (might have been from a shipping cap, not sure though) in a filter sock once causing hard starts. Personally I would drop the tank and visually inspect rather than guess.