Nick this just happened to two of my cultures too. It will probably be difficult, if not impossible to salvage any springs from the cultures. You can try by picking up you chunks of charcoal and blowing the springs into a new culture, I have found that the mites are better at hanging on, but its the springtail hailmary.
I have heard that the guys using ground mushrooms don't have mite problems but I have never used mushrooms, so I don't know. I primarily use flake fish food, but the down side is that mites like it too. I have been reading about mites lately, and apparently mites like dry air, so if you have a humid frog room or wet culutres then you are less prone to mite infestations??? I would love to hear some expert opinions on that--calling the bug experts!
I usually keep 8-10 spring cultures going so if I see some get infested with mites, I dump them and start some new ones. I also keep my cultures on trays covered with mite paper, this seems to help too. I will note that I took some of the charcoal chunks covered with brown mites and put them in my tanks, came back in a few and they were surrounded by pumilio going to town on the mites. In the end, you are probably best dumping the cultures and starting over.