A likely suspect ...
It happened again, on my desktop PC this time. Call this 1.5.2.336 iteration HUNG.
I started the 1.5.2.335 version. Call this iteration PRIOR.
I started the other 1.5.2.336 copy. Call this iteration TEST.
All three iterations were running at the same time.
Observations:
1. HUNG and PRIOR share some directories (Backups, Settings, Cache, Tasks, Snapshots). TEST has its own directories.
2. All three iterations had finished license processing (based on title bar contents). All three have their own copy of the license.
3. HUNG behaved like this: HUNG behavior -- PRIOR and TEST behaved like this: NORMAL behavior
4. TaskSwitch.exe showed two tasks for each iteration. When PRIOR and TEST were minimized, they only had one task (therefore, the second task for each was its window). HUNG could not be minimized since it was unresponsive, so it always showed two tasks.
Conclusion:
The most significant observations are at the linked-to posts in 3 above.
It is now more than 50% certain (in my opinion) that the HUNG bug is in the BackupPruning process (or whatever PT is doing when it cycles through the Backups subdirectories and opens files there). :)