I guess I didn't get it from your posts above...
If you leave the jumper wire on the Fp and B+ terminals in the diag port, will it run fine? I know you said that if you "prime" the system by doing that it runs for a longer period of time, but did you leave the wire in place? The reason I ask is that you may have a faulty airflow meter. You might try leaving that jumper wire installed and see what happens, if you haven't already.
To test for fuel flow, I'd reccomend tapping into the cold start injector line and seeing what kind of volume of fuel you get before you go to the trouble to drop the tank and inspect the pump/sock assy. Also, FWIW, a stock 87-92 Supra Turbo fuel pump fits right into that tank...I've got my stock Supra pump in my truck, as I Upgraded to the TT Supra pump when I rebuilt my Supra engine...
I'm a Toyota Mechanic at a local dealership, so let me know if I can help...
Ryan