Hi Kate, and welcome to the Forum.
What sort of condition were your exbatts in when they arrived? It sounds as if your girl has gone into full moult, which would be normal at this time of year. Newly rehomed exbatts can look rather weird, poor girls, until their true beauty becomes apparent as they recover their plumage. They are also likely to be low in essential nutrients after their 'career' on the fast track of an egg production line, and maybe stressed by all the changes in their lives, lucky though they are. This may reduce their ability to re- feather, as growing feathers takes a lot of resources from their bodies. Maybe you are going them some kind of vitamin or dietary supplement, such as Poultry Spice or Nettex Mineral Powder with probiotics?
What I'm trying to say is that bare patches are common anyway on newly rehomed exbatts, and of course the main problem to watch out for is if any of the others start to peck at them. If blood is drawn they will all pile in and you will have a big problem. But as you say it's just red and sore looking, this may not be happening at least at the moment.
Red mites don't live on the hens' bodies, they just crawl out of the housing to feed at night and then hide away next day. Of course they can cause great pain and discomfort to the hens, leading to anaemia from blood loss if not treated. But as you say you are aware of the outbreak and dealing with it, there may be some other reason for her irritation. One possibility is Northern Fowl Mite, a small mite which does live on the chicken and causes various skin problems. See this article on the main Poultrykeeeper website (the link to the main site is at the bottom of the page,) and the article about Northern Fowl Mite is here
http://poultrykeeper.com/external-problems/northern-fowl-mite
If you examine her and think this might be the case, you will need to treat all of the girls as they are highly contagious. Let us know what you find, and other people might have alternative suggestions for you. If no sign of mites, and she seems happy and not bullied, then maybe just help her through the moult and a wonderful new bird will emerge in a week or two's time!