I went back, tried again, and wrote down the error message.
When I set the config I want, and reboot, the dialog that comes up on the log-in screen says:
"Could not switch the monitor configuration
could not set the configuration for CRTC 149"
When I then login, and go back into the Catalyst Control Center, and switch to the "Display Manager" view, a dialog pop up that says:
"AMD Catalyst Control Center has automatically configured your system for maximum desktop size.
Press Apply in Catalyst Control Center to accept this configuration or Cancel to revert changes."
When I dismiss the dialog, I see the settings have automatically had the third monitor disabled, and the desktop size reduced.
It seems like some logic in CCC knows that something is up, but it won't say what?
If I then re-edit the settings back to how I want them, it tries to do it (no reboot required this time), fails, and gives another, different error message:
"Invalid Settings
The current settings cannot be applied. Possible issues may include:
- Display(s) cannot be enabled.
- Setting(s) cannot be applied due to insufficient video memory."
I don't understand this: like I said, the open-source "radeon" driver can drive three monitors, so why can't this driver do it? 
Any help much appreciated!
BTW, is there anywhere better to ask this question?