Misfire
Replaced plugs, ran better
Misfire, then deteriorated, would not run
Codes for O2 sensors
Replaced both downstream O2 sensors
Codes for crankshaft position sensor
Replaced CPS
Replaced coolant temp sensor
Verified fuel pressure with in-line gauge
Discovered distributor rotor ball bearings had disintegrated, with fragments in distributor
Replaced distributor (thought this was the issue)
Verified timing
Had ECU tested, results bad ECU
Replaced ECU with "verified" used
Replaced ECU relay
Took to Infiniti dealer
They could get it to run (very roughly) by disconnecting crankshaft position sensor
Recommended replacing crankshaft position sensor (that had already been replaced)
Did not work
Recommended replacing ECU and distributor (both of which had already been replaced). I declined
This QX4 is in pristene condition otherwise. I've completely rebuilt a half dozen other engines, so not a novice. But we (including dealership) are stumped. Help.

You have to be dealing with pinheads who can't read or don't care. The VG33 crankshaft sensor isn't used for any operational purpose. This is a direct quote from EC-277 in the FSM:
The sensor is not used to control the engine system. It is used only for the onboard diagnosis.

The main thing it provides is the tach signal, so if your tach works, there's nothing wrong with the CKP. Even if it didn't work, it wouldn't affect starting or operation in the slightest. The fact that it ran badly when the CKP was pulled meant absolutely zero, it was a coincidence.

It sounds to me like you need to go back to basics. Start with a scan so you know what the ECM is thinking, verify fuel by squirting some Brakleen or Gumout down the barrel, verify power and (especially) ground at the distributor, verify spark coming out of the distributor, verify spark timing with a light, pull the MAF connector and verify that isn't causing the problem, yank the front O2's to see if it starts without them (meaning your cats are clogged). Once you have a few things ruled out, you can start chasing whatever isn't.

Have done everything you've suggested (and more) except pulling front O2s. Will try that. Thanks