ruined a phillips screw, any inspired solution?

Not strictly audio but related and a real mess. I wanted to open up the cabinet of a cdp to change a tube inside which involved removing 6 small phillips screws with a recessed head,... and of course, there is always one that pretends to be sword Excalibur. Sadly, after I had attacked it with every imaginable screwdriver, I noticed that I had literally milled out the head. So I now have an unbudgeable screw with a perfectly round cavity on the head sitting on a rather sensitive piece of gear (the plate I have to remove holds most of the electronic circuitry, the cd drive and the tube, go figure). Anyone faced a similar conundrum and solved it?
Thanks for not laughing 8^(