If you've checked with an accurate mechanical gauge, (not the dash gauge) and the readings are accurate it could be a few things. The bearings could be bad, or going, or the pump could be starting to go, or clogged screen, and not be able to handle the hot thin oil. Now since you said thicker oil didn't matter when it gets hot, (low pressure), my guess is the oil pump could be bad.
Checking bearings is not an easy job, if I were pulling the oil pan I would probably change the oil pump and screen and see what happens. The good news is there is no knocking noise when the engine is hot or cold, no oil use, and it runs good.
Before I drop the pan I would check pressure with a good mechanical gauge.