If the intermediate shaft broke...you would have no oil psi. If the gear on it went south, you have no running engine because the cam turns both the distributor and oil pump and if that happened your timing would be so far off it wouldn't run...and besides, the mp hardened intermediate shaft gear is pinned so that gear can't spin loose from the shaft , gets rid of that old problem but still leaves the possibility of the motor running without oil psi...but we can install a psi kill switch if we wanted to, but point is those things are not the problem.
Debris in the pump relief is my first guess.
I ask about the crank end play, because I'm wondering if you wiped the thrust bearing out...but you would have oil psi still, the crank would hit the block before uncovering the oil passages/feed. You have not mentioned any crank walk or noise...that kinda rules that out.
It would be something else to find out you have studs in the mains and that rear one sticks up not letting the pump sit flush....that would be a doozy of an overlook.