Booted into Safe Mode
Booted into recovery mode and ran DU first aid
Ran Apple Diagnostics.
Beachballing remains--and for the simplest of tasks: just clicking on Finder, or typing in a web address in Safari.
I've even tried to run Linc's shell script, and even it won't complete--getting only through the 1st of 4 parts after 45 minutes.
surely this can't merely be a signal call for a memory upgrade to 16GB (running an iMac late 2013 21.5)
ideas?