I don't know about limestone, but my farmer-friends tell me I can use food-grade lime (maybe the same stuff?) in my run. I haven't tried it, yet, mainly because they follow the recommendation with a warning to cover the lime with other bedding. Apparently direct contact of lime on chicken feet can cause irritation. Seems counter-productive to me!
I conquered the mud issue by adding pine needles and leaves to the floor of the run and building a small berm along the back end to block drainage. I also added some 3-6 inch high tree stump pieces so my birds could climb up if it gets wet again. So far, so good!