Ok. Problem identified and solved.
After the chips were programmed, when they were re-inserted into the programmer, they started executing the code before going into program mode. Once the code started executing, it was impossible to get them into program mode.
Solution: The positive side of R4 on the P16PRO40 has 13V on it. I took an aligator clip and a wire and directly applied 13V to PIN4 of the 16F628. That forces it into program mode on power-up before the code can execute. Then the chip can be erased, jumper removed and the chip can be programmed. I was able to resurect 6 chips that I thought I'd fried.
Question to the community:
How do I prevent this in the future? I've read it has something to do with MCLR?