RESULTS: So, I'm not entirely sure what did it? But somewhere between the dishsoap+hot water and the baking soda, the smell went away.

At first I thought the dish soap was making it worse. So I dumped the baking soda in the with the water, and mixed it around, and left it there. And it still smelled pretty bad when I went to work, but by the time I came back home, it had mercifully dried and I couldn't smell it.

And then I left it for a couple days, because I was tired of dealing with it. When I came back, I dumped some vinegar on it, and the baking soda fizzed very satisfyingly. But I don't think I even needed the vinegar---there was no trace of the smell at all anymore.

So, in conclusion? Some combination of dish soap, hot water, baking soda, and plain old time seems to have taken care of the smell.