How to move a Time Machine sparsebundle on a networked machine
I was able to solve this by following Pondini (http://www.baligu.com/pondini/TM/18.html#id18) with a slight modification.  Instead of copying the Backups.backupdb folder from the top level of my source partition I copied it from within the original sparsebundle (what I called TM.sparsebundle above). This worked flawlessly.  

It would be nice if there was a faster way to accomplish this - essentially some way to tell TM that a particular sparsebundle was to be used by TM.  But at least this heavy-handed method works.