Okay, AVTS 3.13.1 is still not quite ready, but I have a consolation prize. The original intention was to have 1.16.2 be incompatible AVTS 3.12.x, as has been the case with protocol changes in the past. That really is cruel and unusual for the install base though.
The GEMS 1.16.3 release should now download to both 3.12 and the soon to be released 3.13. Of course, once downloaded, you still can't swap floppies between systems with different versions.
Note that the download protocol is almost guaranteed to change in an incompatible way at least one more time in the future. Just not this time.