Removing stripped set screw on shower handle

I am trying to remove this old diverter valve handle from a shower. The manual shows it should be a 1/8” Allen wrench but it may be stripped because I can’t get the wrench to “bite” onto anything. I have tried different size Allen wrenches and small screwdrivers, but it still won’t come off. The handle is fairly loose to being with but I can’t back the set screw off enough to remove the handle. Ideas?

https://imgur.com/a/JVyNIcw