Thanks! It's good to get confirmation that it would be necessary to use scripted mouse clicks and the GetClickablePoint() function.
I've investigated it briefly (using Visual UIA Verify) and although it looks as though it will be slightly convoluted, I think it will be doable.
One other thing I had wondered about, is that maybe it would be possible to implement the UIA GridPattern by implementing the System.Windows.Automation.Provider.IGridProvider interface. Do you have any experience about that?