Mike, for super-glue problems like that, you need acetone. Lots of it.
Something similar happened to me a few weeks ago: while I was trying to repair a broken keychain, my tube of super-glue suddenly burst and spilled fast-setting adhesive all over my right hand. I simply washed and rubbed in acetone till I’d gotten most of it off. It took several hours, and my hands were freezing from the quick evaporation of the chemical. (It’s a bit like formalin.) What didn’t come off was weakened enough by the acetone to get peeled off a few days later. However, some of the glue got permanently bound to my fingernails. To this day, I’m still waiting for a few super-glue bumps to grow off with the nail.