Problems solved, This was a write up from Dan from Main Street Amusements in Lafayette Indiana.
Another Williams sound board back in action - hopefully! This one was a lot more work than the previous one. It's problem was intermittent, and intermittent problems are always tougher to track down. After verifying that the socketed chips were good the next step was to replace the AMI brand PIA chip. With a new PIA and socket installed the board was running its self test perfectly - until it wasn't. It ran for almost an hour and then started making random weird sounds.
After doing a bit of troubleshooting the next logical suspect was the RAM chip. And look, it's an AMI brand chip! AMI PIAs are garbage, so it's not too big of a jump to assume the same about their RAM chips. Replacing the 6810 RAM chip seems to have fixed the board, but because of the intermittent nature of the problem I'll start the self test and leave it running, for a l-o-n-g time.
Usually I just cut these old chips out, but to hopefully verify that it was indeed bad I removed the 6810 chip intact. After installing a new chip socket I re-installed the original 6810, and the intermittent problem was still present. Replacing the 6810 with a new one seems to have done the trick.