If she is not feeling pain when you cut at it, it's pretty advanced stage problem you have there. The thing might be acting normal because so much has rotted away the nerves are shot too and she's literally not aware of how bad she is. All that rot, she's swallowig it and it's getting into her system too. I don't want to be the danny downer here but I think this is a dead bird walking. Don't be surprised if maggots show up soon, because the flies will smell that rot and lay in it too.
IF you decide to do surgery, super glue will hold the skin together over the wound, it can hold flesh together too somewhat, just be careful when applying you don't glue your fingers to her, and cause more tissue trauma having to rip your glued finger out of her... whatever.
Good luck and I hope she gets better but this sounds so bad already.
Aaron