In case anyone stumbles upon this thread in the future, here's a quick update:
Our cochin is almost fully healed! We've had her in a medium sized dog crate since the incident, spraying her with vetericyn a couple times a day to ensure the wound doesn't get infected. We'll be re-introducing to the coop her in the next few days as soon as the obvious redness is gone.
It turned out that we had one bad bully who was really the perpetrator here. We kept her separated as much as possible for a few days, and routinely check in on the coop now to make sure that behavior doesn't start back up. We also built a new feeding system with twice as much space for the hens. We only have four hens, and the last system wasn't exactly small, but we wanted to take away anything that could've been cause for aggression. After all of this, they seem to be pretty peaceable now, so I think we were able to nip this problem in the bud for the most part.
Thanks everyone for your help!