@chanadler I was having the exact same problem today and I thought I was done for. However I was able to successfully get the screw out using needle nose pliers and a small flat head screwdriver.
Essentially I used the needle nose pliers to rip out the thin plastic which surrounds the screw hole.
[image|1201105]
My original intention was to use the pliers to get a hold on the screw, but that quickly proved to be impossible. Then as a last ditch attempt, I used the small screwdriver as a lever to get purchase on the now exposed side of the screw.
[image|1201108]
If the gif above doesn't play you can see it my very shoddy but effective attempt here: https://imgur.com/a/1Rz8B