"I'd be every bit as willing for a dentist to be drilling as to ever let a woman in my life." This solves the redundancy and the as/than problem without altering the rhyme, the rhythm, or the meaning. The split infinitive, to me, is inconsequential--everybody does it from time to time--even grammarians--in agitated speech as opposed to careful writing.
Believe it or not, I once came up with that same correction of the lyrics, and I do agree if it's a good job if one doesn't mind the split infinitive. (Another poster here would still object to "willing for," but I'm not entirely sure that's an error.)