Oil flow problem

Any oil going to the cylinder head has to pass through the oil filter so I am surprised you mentioned no oil going through filter.

How did you come to the conclusion oil is not going through the filter?
Is engine heavily sludged?
Do you use any form of oil treatment?

Filter is bone dry and as clean as the day I installed it. Yet I can see oil splashing around inside the head when I run the engine and remove the oil filler cap.

No - I do not use any form of oil treatment & I run Mobil-1 5W30. The car was purchased used. 125k miles when I received it, 135k now. I pulled the valve cover and it had modest sludge so I cleaned it all out, no idea about the inside the case.

I am as puzzled as you are.

Remove the spark plugs and oil filter. Crank the engine and note if oil comes out of the oil filter base. This would verify of il is getting to the filter.