Just looking at the two bolts (Yes, I apologize, they ARE bolts!) it appears there was maybe 1/4 -3/8" inch of bolt protruding above the nut at the top when inserted. If you don't want to try a screw extractor, you could cut into the wall (probably on the inside of the top) to gain access to that part. Apply a liberal amount of penetrating oil, wait, apply more, and repeat. Finally, with a pair of vise-grip pliers, you might be able to work the bolt back and forth a bit to break it loose. Then you could probably use the same pliers to screw it UP, bringing it out of the top of the nut.
You could then replace the part of the interior wall you took out and could refinish it so that it would not be TOO noticeable.
I agree with Gary - DO use anti-seize on the bolts you reinsert! Just looking at the condition of the bolt that came out - I advise you to replace them all. I think I'd use "hardened" ones (grade 5 I think?). You won't need to torque them in too firmly, so just "snug" them up.
- Jack