We went to the vet this morning.
GREAT NEWS: We have a (non-board certified) avian vet within forty-five minutes of our house. She has been seeing parrots for 10 years, has an african grey, and has at least one parrot patient per day. That is an HUGE improvement over our previous experience calling around. The only way I found them was by looking at google reviews for every vet office within an hour of my house. For whatever reason, they don't promote this vet's expertise on their website, even though she has tons of experience.
GOOD NEWS: We did a culture and have identified the problem as a yeast infection. She'll be taking oral meds for 10 days. Also, the knockoff SSD cream I found on Amazon was approved of by the vet, and we were told to keep using it.
NOT-SO-GOOD NEWS: We have to give oral meds and Cord does not love it. I wish I'd been training that as part of our husbandry tasks. After we're done with the meds and she has forgiven me, I'm going to look into adding this to our repertoire.