I don't think there's going to be an easy way to over-ride the
default "transparent" behaviour of BBEdit/Interarchy to solve your
problems. That is, whatever you come up with may not be able to be
mapped to the application's "Save" command itself.
But what you want to do is essentially trivial, when looked at as an
Applescript problem:
"Can I create a command, which can be called when editing a file
in BBEdit, saves the file to an FTP server, with a given prefix
or suffix on the filename, then renames two files on that server?"
the answer is definitely yes and should be short work for AppleScript
/ BBEdit / Interarchy gurus. You're just asking on the wrong list,
that's all.