Fist things first: let's eliminate the check valve or whatever the reason it isn't holding pressure with the ignition switch turned off. (I had a bad check valve on a brand new fuel pump once. Just because a new part was just installed,, you can't assume it works properly. Anyway, with mouth back pressure on each individual pump, the pump with the bad check valve was immediately discovered.)
Then I'd want to hook a fuel pressure gauge to the fuel rail and tape the gauge to the windshield and go for a drive. At light throtle, pressure should be mid 40s. And, at WOT you want to see low to mid 50s. This will verify the entire fuel delivery system: pumps, regulator, filter, and fuel lines. Failure to provide pressure means isolating each delivery part and verifying they each are working. (My fuel filter was nearly plugged at just over 40k miles.)
Unless you install a "secondary delete" chip and tie the SPTs open (tie-wrapped), the integrity of the SPT system is important. You can get by w/o the vacuum pump upon initial WOT operation. But, depending on how tight the vacuum network is, the secondaries may not stay open without vacuum from the plenum or the backup pump. (And, you should then get an SES light and a code 61 (no vacuum).
So. Fix/replace the pump and assure the integrity of the rest of the SPT system first. Or! Elimimate the entire SPT amd install a "SPT DELETE" chip (and NEVER be troubled with it again).
Enough 4 now. Ned to a eliminate the fuel issue first.
