I've got the whole SB on disk. Just played the Dr. Seuss segment. I'm usually pretty good at "Name That Tune," but I've never heard that before in my life. It's pretty generic, whatever it is. Sounds vaguely like something Yanni (or his "disciple," John Tesh) would do.
Now that I've heard it, it's driving me crazy too, not because I want to know the name, but because it is SO ANNOYING.