Well, go figure. I think I've answered my own question. I'll post it via edit here in case it helps anyone else as soon as I collect the links.
Here it is.
The answer seems to be in the underscan and overscan options in Catalyst, and which are part of the scaling features. I'd seen them but hadn't played with them, 'cause stuff about graphics and monitors basically sends me running for the nearest cover.
I hadn't been finding anything recent or directly on via Google. But I finally Googled … the title I put on this thread. So I found this, which is a recent post on Tom's Hardware …
http://www.tomshardware.com/forum/30...ng-full-screen. It refers the overscan option and links to this, which describes it pretty well …
http://www.aoclarkejr.com/ati-cataly...n-options.html .
At any rate, I tried that and I now have full screen on 1920x1080.
Hope this helps someone.