I am going to jump in on the gangrene question. As someone with over 30 years experience as a microbiologist including many in hospitals, maybe I can help clear up any confusion.
Just to clear this up there are two types of gangrene, dry and wet. In humans, Dry Gangrene is the type typically found in diabetics where blood flow to an extremity is lost (usually a toe first in diabtetics). The tissues dies, turns black and falls off. While we don't want any of the birds to lose their toes, it is most likely that process which would occur here. Blood flow is lost because of the freezing, the tissue dies, turns black, and falls off.
The second type of Gangrene is called Wet Gangrene. That is much more serious because it is caused by a bacterial infection. It is typically caused by a bacteria called Clostridium perfringes. Clostridium perfringens is a bacterium that can only survive in the absence of oxygen. Once infection with Clostridium perfringens (CP) starts the bacteria releases a toxin that kills the surrounding tissue in order to create a pocket where blood no longer flows thereby eliminating the oxygen which blood carries with it. Tthis enables the bacteria to spread and grow. CP infection is usually accompanied by pus and the smell of death. I can think of no other way to describe it. The first time i smelled it in the ER i knew right away. Sometimes CP infection will result in gas pockets building up in the body. This is called Gas Gangrene.
So how do you rule out Wet Gangrene in this case? Is there a nasty green pussy discharge? Does it smell awful? Is it swelling significantly? Is it still bleeding? If is smells, has a pussy green discharge, is swelling considerably and you see no blood flow, then you must treat with antibiotics. None of the photos I have seen so far lead me to the conclusion that this is a case of Wet Gangrene at this time. In fact, the continued application of antibiotics should help to keep that from happening. You are doing a great job treating them. Stay the course and let's hope the damage has been limited by your actions.