Don't use epoxy! The resulting 'plug' of glue will actually be harder than the surrounding wood, and when you try to drill a new pilot hole for the screw, the drill will step off to one side.
I never thought about the that. Excellent point.
Today I bought a 1/8" dowel from the craft store. It fits in the stripped hole very well. I am going to cut it to length and give it a try. Should work well.
Thanks for the inout everyone!
Shane