What I'd like to know is, can I buy a replacement opener that will work
with the existing chain? It would be a lot easier to replace just that
unit than to have to replace the chain, springs, etc.

It can be done as long as sears still sells that type. I did the same
as you are inquiring about a few years ago. Your existing rail will
hook directly to it. You'll also have to install the supplied door
safety lights.