i should be working (but i'm fixing my computer).

It turns out my problem with the travelling gnome panels is not entirely "unpredictable."

...

It occurred to me that I had made a panel change coincident to the problem emerging. So I tested it again.

I had decided I wanted panels that did not go the full length of the monitor. So, I unchecked the property box "expand."

When I did that, nothing untoward happened. The panel shrunk down to accommodate the icons on it. This was good -- I wanted some separation between panels on the various edges of the screen. For instance, I have my kicker panels set at about 90% and centered.

The edge-shifting did not occur until I logged out and logged back in, so I did not make the connection immediately.

However, after I rebuilt my gnome panel(s) to a single panel at the bottom, which stayed there just fine, I was looking at the screen wondering what I had done differently. Also, I had tried to recreate the bottom and right panels -- and immediately ran into a problem with the right one, but not the bottom one. Hmmm.

Well, as it turned out, I left the bottom one "expanded" but I shrank the right one. And, the right one promptly moved to the left on re-login.

So, having made this observation, I added a new blank panel to the right, logged out -- and on return, there it was on the left. Furthering my experimentation, I clicked the "expanded" properties box, THEN tried to move it back to the right -- and sure enough, it zapped over to the right.

Mystery solved.

Who'da guessed?