I agree that it's often helpful to ask on a forum and see if anyone else has had the same experience. But having hit a blank there is the whole of the knowledge of the internet available if you feel that consulting your vet is a waste of time. It would seem of little help to the hen just giving up because your vet is of little use with poultry.
I googled "large black growth on hen's face" and found the picture below on "Back yard poultry"
Looks very similar to your's. The suggestion is that the growth is a canker and treatment with Metronidazole might help. I believe you can get it from pet shops, as a treatment for fish infections, under the name of fish zole. Available, apparently without prescription, as your vet won't prescribe it anyway without seeing the bird, and that would cost more than the bird's worth.