The question is: how does umount(8) *know* the file system type?
Currently it gets that from the kernel.  In the case of your "snfs,"
it sounds like you don't know.

Perhaps it makes sense to put a PID in the "mount arguments" handed to
the kernel, and have umount(8) check that.  This could be useful for
shutting down some other types of file systems as well (AFS and some
FTP translators come to mind).

It also means you don't have to worry about where to store and how to
name "PID files" for each mount.  :-)