I did delete all but the most recent and seemingly correct files, as suggested. Things have stabilized. It now seems only the Trash moving itself to the upper left corner each reboot over the past few days.
BTW, after a general update, e.g. in the last week, lots of movement.
Bottom line: Mostly stable now. I will hold off freezing the icons unless things get difficult again, but it is very helpful to know about that.
This is an annoyance that reappears in this desktop, and needs attention by developers when they can.
Thank you for the good suggestions everyone.