Thanks for your commiserations, Terri. I may have brought it on myself by not cleaning out old files more thoroughly.
But there has been some progress. I was on the phone with Apple Tech Support again this afternoon. She was about to have me wipe the SSD and start over but first suggested I disconnect all five peripheral hard drives and test the issue. To my utter surprise, that seemed to fix it. I then reconnected them individually, but was unable to isolate any particular one as causing the problem. As of the moment, four of the five are connected and I still have no permissions problems.
Seriously, IMNSHO you really need to rethink that whole idea of having all those external drives connected to your computer all the time.....I can't think that it is really necessary, and it certainly does seem to be a factor in the problems you have from time to time...... Why make (computer) life more complicated when it doesn't need to be?