I've not used sulmet for cocci, as it is much harder on them. I always use corid. For corid you need to give a fresh mixture every day as their only water source.
The important thing is to treat for the entire recommended time at the correct dose, whatever you use. Given the choice, I'd personally use corid.
There is no way to remove the cocci from the soil. If your coop has soiled shavings or bedding I'd clean all that out and replace. Same for any build up of droppings. And make sure it's dry.
I pretty much only use vinegar to clean my coop.
When I'm raising chicks in a brooder I give them the sandy soil from my yard, not from the coop area to dust bathe in, in a large heavy plant saucer. Easy to dump and clean.
As they get closer to going out to the 'big house' I start adding in small amounts of dry dirt from the coop area to their bath saucer. The idea is to gradually expose them so they have a chance to build up some resistance. You will have to just be observant and watch for the signs of illness. When they first go out I do not put them out if the ground is wet or has been wet for a couple of days. I also start with short days out, and then back to the brooder, and build up their time on the ground. Maybe overkill, but it's a system that's worked well for me.
Chicks are more susceptible than older birds, and new birds to your flock will be susceptible. They will build resistance, but it can still happen to any age bird. I'm always vigilant after a period of rainy weather, as the wet/damp ground seems to encourage a cocci bloom. I always follow up treatment with vitamins and probiotics in their water.
Best of luck.