There are 9 types of coccidia that can infect chickens. There are 2 types that do not respond to Corid and require a sulfa drug to treat them. The sulfa drug provides antibiotic action to treat the coccidia.
Just for your information; coccidia oocysts will always show up on a microscopic slide. However, if the slide is loaded with oocysts, then there is a problem which requires treatment.
If you havent used the Corid yet, go ahead and get them started on it. If you havnt seen improvement after the fifth day, get them started on the SMZ-TMP per vets instructions.
I agree with you regarding removing the organic material, too much work...and I personally know about a sore back. I just got through having lower back surgery this past January for years of having a painful lower back. No more!

However, keeping everything as dry as possible is imperative when it comes to chicken keeping. In your case, I recommend that you scoop poop several times a day in your pens as best as you can. It will help deter coccidiosis and other bacterial issues.
I have sand in all my chicken pens, coops and some of the nest boxes. Sand deters parasites, doesnt run off nor creates nasty mud puddles after it rains that chickens love to drink from. It's very easy to scoop poop and dispose of it in a five gallon bucket.
Cleaning out the coops each morning, keeping feeders and waterers feces free is key in deterring coccidiosis and other nasties.
Here where I live, our soil is moist/wet and warm most of the year, worm soup. I worm my birds monthly with Valbazen. I have used Safeguard and other wormers over the years without any problems, but Valbazen is my go to wormer.
I see no need for you to worm your birds since the slides were clean.
@Eggcessive beat me to the punch and gave you excellent advice, she's a faster typist than me lol.