Doesn't sound like any fuel pump issue I've ever heard of.
Sounds like a fairly normal priming issue with the 545RFE for the delay. The stalling issue could be a dirty TB and/or failing TPS or IAC valve or it could be a transmission issue. The subtle nuances of how it's stalling could tell whether to think trans or engine, but that's about impossible to troubleshoot with a keyboard.
08 5.7 Limited - Intake - Exhaust - SC Tuner - BT catch can - 5100's - white LED dash and lighting