Just to summarize my understanding:
- Seem obvious that there's an issue with getting power to the fuel pump while cranking/running, but...
- Two different fuel pumps wired directly to the battery will start the 100, but...
- When it starts, it rapidly ends up sputtering and dying, even though the fuel pump is still humming along happily.
Based on these facts, it seems you may have two problems that may or may not be related. First is the issue with power to your fuel pump: as someone else has stated, you need to chase those wires as best you can and figure out where there's a break/corrosion/etc.
I think your second issue may be crank/cam sensor related, and may be tied into your fuel pump problem.
MOST ECUs run the fuel pump for a couple seconds to prime the system when you turn the key (I don't know if the 100 does this). Then, when they detect RPM sync (basically, when they see a signal on both the crank sensor and the cam sensor that makes sense), then the ECU turns on the fuel pump again. No rpm sync, no fuel pump.
However, you could be getting and losing RPM sync because of bad grounding or a bad sensor. When the fuel pump is connected to ECU controlled power, it's not enough signal to switch on the fuel pump. When you hardwire it, there's enough rpm sync to fire the plugs for a bit but then it loses sync again and the engine dies.
I think someone else said it, but I'd be ohming out all your crank and cam sensors, and check their wiring for continuity or damage, and seeing if there's an issue there.
Edit: I'll just add, codes can be incredibly useful for this sort of thing, but a lack of codes doesn't mean much either. Don't take it as truth either way. Good luck!