Here's what Bill told me to do:

1. Take the saddle off the bike.
2. Turn it upside down.
3. See the threaded bolt thingy? (in the nose) Wiggle it. The end of that bolt is round, and sits in a cup at the very front of the shackle in the nose. It's meant to move freely within the cup.
4. Did you hear your noise? (it'll be quieter than on the bike, but I heard some of my noise just FINE)
5. If that made noise, drip oil or smear grease into the edges of the cup/bolt at the very front of the nose. (I used T-9, which is Boeing's version of White Lightning.) It will work its way in.

Next:

6. See the funny silver folded thing just aft of the cup and adjustment nut? See how it folds around the end of the bent rod that is the rails and frame?
7. Wiggle whatever you can there. (I wiggled the rail).
8. Did you hear more of your noise? (I didn't.)
9. Whether you did or not, drip some oil in there anyway. Can't hurt.

Finally:

Put the seat back on the bike. Do some of the stuff that you know made the seat creak before. Is it better? Good. Repeat the above as necessary to make you happy.

Still noisy? Call Bill. Some seats are just noisy, for whatever reason. He will try to help you more specifically over the phone, or replace it.

I was just CERTAIN that the noise was coming from under my butt, not from the nose. But it really was coming from the nose, I just felt it under my butt. After riding a few times I can now hear just the faintest little snap again when I'm rocking in the saddle (climbing the Evil Hill of Doom on my commute, bad form I know). Bill said grease was best. I didn't have grease, so I'll just keep applying T-9 until I built up enough wax in the cup to get rid of all the noise.