I have a muddy run too, and can’t honestly say I know what to do for it, BUT I would STRONGLY advise against using bedding from your other pets. Germs, worms, and parasites carried by different species can be a major issue in old bedding, especially cross-species. A bug in one animal’s gut may be lethal, and a different animal might be an entirely asymptomatic carrier. You’d never know until your chickens got sick (or, for that matter, you did).