Todd,
I've been digging on this for an hour. I have yet to find a lube circuit diagram for that motor.
Of coarse, in a Kohler manual, they have it. Not Onan apparently.
So, here is what I can tell you. Good rule of thumb for oil pressure is 10 PSI for every 1000 RPM. So, you should get around 5-10 PSI at idle, and 30 or so WOT. Yours looks a little low. Being that you pulled the spring apart a bit and it got better, I'd say your spring is shot. It likely lost pressure after running due to working out that assembly lube and also because the oil warmed up. I'd say replace the spring and see what happens.
FWIW, I NEVER overhaul a motor without installing a new oil pump. Can't live without oil pressure.
On your comment about a loose tolerance causing low pressure. Yes, it's possible. I'd be looking at the main and cam bearings, but they are all new. No way to check clearance on them though. So, hopefully the clearance was correct. I didn't take time to refresh myself on this rebuild, but were the main journals on the crank ground? Did you check the max wear limit on the cam journals that ride on the bearings? Both would be places for oil pressure loss. And no.... if something was loose, you likely wouldn't hear it. We're not talking about being able to rattle around, we're talking low tolerance. .0015" under spec on either the crank of cam and it could have low pressure, but it wouldn't rattle or anything.
Replace the spring and see where that gets you.