My debacle with soaked carpets was starting to turn sour, and I mean more than the smell (I have a mold allergy so this could be a big problem). The carpet was starting to show signs of Petri-fication, as in mold growth. I did a little Google-aided research and found a solution.
I had to go back out to get the noisy carpet cleaner I used this weekend, but instead of their spendy solution, I used a strong solution of Lysol to kill the mold. And it seems to have worked. For one thing, I think this cleaner works better by getting the carpet drier, and for another the Lysol really seems to work. A weak bleach solution would probably work as well but with the risks of colorfastness and vapors.
I am going to let it dry overnight (with a fan blowing over it) and see if it needs another go tomorrow. But early signs look good. Next steps are to actually plumb in the washer discharge pipe so this doesn’t happen again.