From what you describe, it is a possibility the pump could be the issue, that's n easy pull off and dismantle job, check the rotor for scoring and wear, and look at the check valve for crud and stickiness. If that shows no problems then yes go to the next job of dropping the pan, it may be a bit more work but it isn't that bad.
Just so you know, your hint proved to be most relevant for restoring functionality to my oil pump. The relief valve wasn't clogged; ... IT WAS LOOSE!!! The bolt was just finger tight. I guess a sloppy install combined with engine vibration produced this effect. Sooooooo....
I removed, cleaned and inspected the pump. Feeling good suction on my thumb, I packed the pump w Vaseline, remounted it, TIGHTENED THAT RELIEF VALVE BOLT GOOD, drained the oil (DAMN it go black fast!) poured it back in for the moment, left the ignition disconnected and used the starter to pump some oil up top. Then, I started it. ECCE!!! There is my normal 50 psi cold oil pressure!
So, I suspect that the pump just lost its prime yesterday from a loose relief valve bolt, introducing a vacuum leak. NOW, I just need to be sure of my lifters, cam, valves, et al.
I expect I've at least one diddled lifter out of this business. Pulled passenger side valve cover and saw plenty oil pooled nicely on rocker arms, just where you want it from the push-rods. Noted that valve cover gasket was NOT even installed properly, and the little idiot who sold me this ride had tried some crap from a collapsible tube, which he likely tried huffing given the quality of his work. Its a MIRACLE this motor ran a day, let alone since St. Patrick's Day. Again, the bolts were nigh finger-loose. I'm sure the driver side is no better.
Since I'm now clearly raped out of working motor transport by the 2nd Law of Thermo, I might as well get all the damned gaskets for pulling the top off this block. Likely gonna have to grovel to the N-lawz also. No matter, its STILL the best car we could have got for the money, and will be so much better when properly rebuilt.