I've done quite a lot of experimentation this morning. One thing I tried was to resurrect my entire corrupt Application Support folder, but remove the entire "Resume" folder within it. Doing that once again allowed a test transfer to start normally and right away. So again, I've confirmed here that the problem is in that "Resume" folder somewhere. Note: I retained all other files within Application Support, including blocklists, and Transfers.plist, from the problem version.
HOWEVER, and this is a massive however for me, forcing the regeneration of the resume files meant that all data file locations were lost. Torrents started downloading that I already had. I needed to pause them all ASAP. I regularly move torrents all around several external volumes (depending on what the data is). So that means again all data for 2000 torrents needs to be re-verified. This will take hours and hours and hours.

In addition, let me point out there A) there is no key equivalent for "Move Data File To..." and "Verify Local Data..." both of which would be helpful in this case; B) a little AppleScript support would go a long way here.
OK, buckling down here.

(By the way, if there were a menu command in Transmission to rebuild all resume files, that would be swell, no? then it would retain path locations, and re-check all data. So easy... )