No word from either of the two companies from which I am trying to obtain music licenses. I guess they just don't want my money. But then again, what would you expect from a company that sues people for parodying songs that are in the public domain.
Happily, I have discovered that copyright law makes granting certain kinds of licenses mandatory. So I can't use the original recording, but I can hire a band to record a cover version for me. Cool! That will almost certainly cost less, and might even sound better. (I've always wanted to tweak one of the lyrics in "Comfortably Numb". It should be "When I was a child I caught a fleeting glimpse/Out of the corner of my MIND.")