The King is dead, long live the King! I always thought that was stupid, but Debian Jessie has gone and the new stable version is Stretch. My main computer is always on 'testing', but the second computer was on Jessie, the old stable. I was using that computer mainly for video processing, but now it's mostly for storage. Anyway, I changed the /etc/apt/sources.list to Stretch, and let 'er rip.
aptitude update and aptitude upgrade gave me an awful lot of upgrades. There were endless conflicts, but then it recommended aptitude --full-resolver, which fixed a lot. Still mucky, and I did a few 'aptitude -f install' commands until everything was clean. All working!