@shingle @dan0 you guys are too funny. It's great working with you all :-)
@foxmccloud there are really not to many options. I don't think that any rubber band or super glue will work for you. Neither one of those things could take the torque needed to remove the screw. What you do want to try is a NEW screwdriver and you can even try a size bigger. It just has to be new. Then push inward while you try to turn the screw loose. If that should not work, you will have to invest in a drill.
Actually, I would get a rotary tool since you can manage that better in this type of environment. There is plenty of room to drill this screw. Remember, you really do not drill the screw out. you just drill enough to separate the head of the screw from the threaded part. If you use a drill bit that is more that 1/2 the diameter of the screw head it will do the trick. You will remove the rest of this screw with a pair of pliers after the back panel comes off.
If you have a any kind of garage or maintenance shop in your area, take it there and ask for some help. I can't imagine that anybody would even charge you for drilling it out. It's a 2 minute job with the right tool