FYI: Corid treats all 9 types of cocci that chickens can get. Sulmet treats 2 types of cocci, coryza, fowl cholera and salmonella pullorum. As Chicmom stated, sand is your best bet to prevent cocci and other internal and external parasites from infecting your chickens. Sand absorbs rainwater, it doesnt wash away, but will settle. We have gulley washer thunderstorms here and havnt had a washout yet. I know all about humidity, we live near a swamp, a river, and the ocean...it is truly unbearable...cant wait for wintertime lol.
Greenkjb is correct about keeping everything dry, that is the key. Perhaps a tarp covering your pen or run propped up like a tent might help keep the ground dry.
Bleachwater will not kill cocci protozoa. If you could sanitize everything; waterers, feeders, thoroughly cleaning out their houses, roosts and nests using ammonia/water mixture...that will kill cocci. Ensure waterers and feeders are rinsed afterwards and the inside of their house is dry and vented before letting your chickens back inside. You could use a fan to help dry and blow out the ammonia fumes. You might want to wear a mask as well if using ammonia inside their house while sanitizing. Good luck.