Well, I gave up on trying to resolve the issues. Thanks for the suggestions, subzero79, wolf2000, and The Master. Unfortunately, I wasn't successful with them. I had most of my notes on customizations, or at least browser links, so getting back fully operational didn't take too long.
I downloaded 3.0.79 and did a clean install. Then, upgraded via Update Management to 3.0.81. "Check" works in both Update Management and in Plug-ins.
Just finished doing a Clonezilla backup of my /dev/sda disk, just in case.
Next step is to install omv-extras. I'll do that using Wolf2000's suggestions for the fix:
wget http://omv-extras.org/openmedi…extrasorg_latest_all3.deb
dpkg -i openmediavault-omvextrasorg_latest_all3.deb