The next day, I found a huge rust ring under my pan. Horrors!!
I scrubbed it with Soft Scrub with bleach. The rust ring remained. Horrors!!
After I finished bemoaning my terrible luck - and wondering how much it would cost to replace my sink - I googled to see if I could find a less-drastic solution to a terrible, terrible mistake.
Several sites recommended an unconventional (at least in my mind) solution - scrubbing the sink with a pumice stone.
Simply wet the stone and scrub scrub scrub. The stone will release fine particles. Don't panic when it does this - it's normal.
You'll have to scrub a.lot.
I still have a bit more scrubbing to do - along with a couple of white vinegar soaks to get it all out. But I'm sure it will be near-perfect in no time.
Note: You should always test out a rockin' awesome solution like this in an inconspicuous spot of sink just to be safe.