What is causing a delayed and abrupt engagement when shifting to reverse?

I agree that it is not idle speed. May be a sticky solenoid that limits pressure buildup.I had the problem on a Bronco when a seal was not installed after the transmission was serviced. Fortunately it is not a frequently occurring condition.

Makes sense. I seem to only have this issue on my job site driving back and forth on dirt and scraps of paper and junk. At home, backing up out of the parking space on concrete never does it.