Well, took it to a local jeweler just to take the case back off. From what I can see, the 10BZAC on the 30-jewel movement is 1950 up to 1966, and the "M3" seems to correlate to 1963. There are also an "X" and "M1" visible on the movement. Not sure what those numbers mean.
Inside the (Omega, as others have noted) case back is a serial number 168010, with some hand-scratched info: "EW-5-2-72" is visible just above the "STAINLESS STEEL" stamping; perhaps this was the last service? There is no family knowledge of why the watch has the Omega back.
There is additional marking (looks almost like pencil, but I didn't touch it) that looks like 40 over A86 over 15J. Not sure what that might mean.
There is still considerable corrosion on the case and case back, especially in the threads. I'm going to carefully clean what I can, and then figure out where/ who to send it to to see if it can be brought back to operating condition to wear.
Thanks again to all that responded.
Ralph