How do I ignore Mouse Clicks with new Unity UI

I created a menu for a keyboard driven game using the new Unity UI buttons. You can navigate with the keyboard and it selects the various buttons properly.

However, if I click anywhere on screen, the buttons become disabled and I can never re-select any of them with the mouse or keyboard.

The buttons all have an OnClick event, so what's also confusing is if I go click on the button itself with the mouse, it also disables the button. It doesn't fire off the "OnClick" script associated with the button.

I want to completely disable mouse input. No cursor, no cursor movement, no button clicks.

Why is this so difficult? I've tried a handful of the workarounds I've seen posted, but none of them do what I want.

If I go with the "reselect the last selected object" option, it visually indicates that a click happened, because it quickly deselects and reselects the image. That's not acceptable.
This is a little disappointing because it seems like something that should be simple to do.