Lol. I agree!
I flipped 'em upside down and they're flat on the mount now. There's no danger of falling.
My bungee idea might not be so crazy if I can find something to use that doesn't look tacky (tacky like a thick purple and yellow elastic bungee). I could put a wedge underneath and strap it down to the mount. Mebbe some black straps or something that I can cinch up. I will figure something out that won't involve drilling.