As an aside, I've been playing around with Button Groups and Buttons.
Inserting 3 Button Groups "sort of" addresses the problem by placing
the buttons in roughly the configuration I'm after. But there's two
drawbacks:
1). The RHS buttons on the top and middle rows are not left justified.
2). The buttons appear with the button image.

1) could be fixed by buffering the LHS with spaces. Not ideal, but it
would do the trick.
2) doesn't seem to have any workaround.

All-in-all, this is not an adequate solution, so... I'm still looking.