Figured it out. It was the factory bulkhead fitting going through the tophat of the fuel pump hanger.
Apparently these fittings are riveted through the top hat and clamp onto a flat disc with a terminal, and this is where the fuel pump wiring attaches.
My rivets got loose, giving me a loose connection I could only identify after removing the fuel pump again. For anyone in the future facing a similar issue and bypassing the FPECU doesn't work, try applying tension to the little caps on the tophat and see if that suddenly gives you power.