I'm not saying this note pertains to your question, I am only relaying my (only) oiling problems in the past.
Years ago a buddy of mine had finished assembling his 454, and I got a call from him that he couldn't get any oil pressure while priming it, and wanted my opinion. I dropped by his house and looked at the situation. I noticed he wasn't seeing much "torque" on the drill motor while spinning the primer (an old modified distributor I loaned him). He was pretty bummed out, thinking that the oil pump or pickup tube was faulty, and he was going to have to pull the engine out again. I suggested that he take the filter off and run the primer a moment to confirm if there was any actual problem with the pump/pickup. Nothing happened for a moment, and then oil gushed out. He apparently had a good size air bubble in the pump that prevented it from priming/pumping. We put the filter back on, and the system primed as expected afterward.
Second story: A couple years later, while autocrossing my '84, I made a hard stop into a "garage stop" at the end of the run. The oil pressure went to zero, and stayed there. I shut the engine off for a moment, and then restarted. Still no oil pressure. Shit. I took a chance that the problem was a similar air bubble (and not a part failure in the engine), and reached under the car and unscrewed the oil filter. Cranked the engine until oil squirted out, and then replaced the filter. Started the engine and had oil pressure. I ordered an Accusump cylinder for it the next week, as I didn't want to risk encountering this issue again, particularly if I was at an actual track day.
Those are just my experiences with the oiling system. Let us know what you find out on your issue there.