If you can locate a working squaretop Vendo 63 / 90 or larger, you can use the compressor for your machine.
They interchange easily. It won't be original to the 81 but neither is the one you have now.
This is what I would do. A vintage R12, OEM, Made in USA cooling deck that will slide right into your machine is the way to go. Plenty of Vendo 63s out there.
