Thanks so much Alex. Your post actually lead to the solution. While probing between the socket frame and socket pin with needle probes the test on the device passed that was failing previously. The pressure against the socket pins forced them to make good contact with the chip's pins. We are going to replace the socket.
Dunkem, I was doing some searching and came across that, and it would have been the perfect solution, but unfortunately purchasing it would require several months in my situation. Good find though. It would have been my ideal solution.