Stopping is important... Right?
 

After sitting for several years, my car had a very soft pedal that needed to be pumped up to get any sort of braking power...

First thing I did was perform a heavy flush of the brake system using a pressure bleeder. This had no effect.

Second, I installed a brand new master cylinder, and performed a re-bleed of the system. Again, same behavior as before. No brake performance until I pump them up.

Lastly, thinking my ABS pump was going out, I ordered some brake lines and a Tee for $75 bucks that allowed me to bypass the ABS strictly for diagnostic purposes to see if the pedal firmed up. I wanted to be sure that the pump was faulty before dropping a grand... Unfortunately, after installation my pedal is still soft.

I have triple checked to confirm that there are no leaks in the system... And the reservoir level is constant, which seems to prove this.

I have bled just the master cylinder, I have reverse bled the system, I have pressure bled the system, and I've bled the old fashioned pedal-pump way. Each time in the correct order. (RR, RL,FR,FL)

Guys, I'm at a total loss of where to go next. Any ideas? What could I be missing?

Ugh how frustrating, eh? Take a look behind your pedal cluster for leaks. Seams you may have a bad seal between the pedal and Master Cylinder.

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What car? Did you bleed the accumulator (if fitted)?

I once had problems with mushiness after a brake flush and pad replacement. One of the members on this board years ago told me to make sure the brake pads are squeezed into place. I had pushed the pistons back into the calipers and just depended on pushing on the brake pedal to tighten everything up. I'd tried everything so I went back and followed his advice. He was right, the mushiness went away.

Using female-female connectors and bleed nipples you can work your way from mc to calipers isolating parts of the system to locate the issue, sounds like theres air still in the system to me.