An Update
Hi all, Thanks to our Workbench, it looks like the mystery is solved! It appears to be a WOW stretched machine. I started digging around, and found the serial number, having been scratched off and painted over. Its a 1960 Singer, serial number HA515075, I think. (Having been filed off before painting, this is as close as I can get.) So, now its time for the restoration process. Thanks for your help!