After a little research I discovered:
My brass is fine.
Dirty primer pocket or clean did not make much difference.
The hand-priming tool easily seated the CCI 350 primers below flush.
The timing of my press is FINE.
The primer plunger is not hanging up.
The ONLY logical conclusion is that the plunger was NOT travelling far enough up to fully seat the primer.
I took a nail and cut off just under the head about a 1/16 of an inch. I then superglued it beneath the shell plate where the primer plunger rests on the frame of the press.
I found that then I had TOO much travel in the primer plunger and it was causing it too stick in up position. So I carefully kept filing down the tip of the nail until I got just an extra little lift on the primer plunger.
I just finished loading 50 rounds. With moderate pressure on priming stroke(much less force than before) I was getting below flush seating with the primers.
I wonder if on some press kits the primer plunger is just a little short causing this hard priming issue...?