[tcrist]

I believe that your car will only vapor lock if it gets hot enough. If it is only running for a couple of min, it should not get hot enough to vapor lock.

That said, Does it have an electric fuel pump? Is it wired correctly? It might be wired to a hot that is only hot when the ignition is in start mode, not in run mode.

If it is a mechanical fuel pump on the engine, You might have some cracked lines and it could be sucking air. That happened to my sons 74 1/2 ton 4X4.

Was the 350 just installed and it just started doing this? What size engine was in it before the 350? V6, 4 cyl?
Maybe you need a more powerfull fuel pump.

Terry