Thank you! Dconf-editor is what did the trick; I was baffled, but the only stupid question is one which is never asked!
I mean, if I didn't want desktop icons, I could have gone with Unity
or GNOME 3
.
I've been using MATE since Mint came out with it, and, having started using Ubuntu with 8.04, was very dismayed that the interface I had fallen in love with was...discontinued. When Ubuntu MATE came out, I started my Happy Dance 
With MATE, I have been able to use my computer the way I want it to run.
Now, I'm going to try to get people to pronounce MATE correctly
!