So I tried to drill out the screw.
Used a tiny bit to try to drill the center for a guide and then go bigger.... and the little screw broke off in the screw... Tried a bigger bit and it just wasn't working... so...
I drilled to the inside where the routing for the tremolo was so I could tap the screw out. After I did that (which was traumatic as hell) I drilled a larger hole to fill with a wooden dowel.
Going to glue in a dowel and bring it home (hopefully) tonight to see if the trem plate covers all the work or not. If it doesn't, I will have to spot paint the dowel and reclear the front of the guitar. As long as it works, I am fine with it. I want to fix it well.
Not loving it, but there is work to be done. Hopefully it will be looking much better around this time tomorrow and be ready to paint.

IMAG0684 by Hentai No Baka, on Flickr