I loved it! I adored it! As soon as I got home, I called the Radio Station, and asked who was performing it. The midnight DJ dug in some paperwork, and said it was probably Big Head Todd and the Monsters.
I've every now and again for the last five years searched the Internet for that track, ever in vain.
Until tonight! About a half-hour ago, I found this:
Offered for free, right on Big Head Todd and the Monsters' website: