OK I think we are getting somewhere! We took the girl to the sink and gave her a nice soak and rinse and tried to play with this thing. The closer we looked, the more it reminded us of a chicken poop. Mealy looking, but this one was hard as a rock. The more we rinsed and soaked, it got softer.
After a bit of time, we were able to start pulling it away in chunks! Eventually we were able to remove nearly all of it. Poor skin underneath was raw and irritated. Gave her one more good rinse and applied some spray antiseptic, which we'll continue to do as it heals.
If it doesn't come back, our theory is: we have a couple of roost bars offset from one another, one higher than the other. It is possible she was underneath another hen who dropped one on her square in the wing. It got gunked up in there, and maybe just a little feather growth and sunlight and it hardened together!
We will report back on her healing progress over the next couple of days. Thank you for the help so far!