Oh boy... don't I know life happens?!!! Congrats on the expanding family! What a blessing. 
I don't vaccinate either... don't want Marek's hiding on my flock. And cocci is irrelevant as a vaccination to me.
But I do think cocci is a possibility and would treat with the Corid.
Though it could be detected by a flock fecal float... and NO you might not have gotten rid of all the worms inside the birds. Round worms and tape are the only two that can be seen in droppings. All others stay in the intestine and only the oocysts (essentially microscopic eggs) will pass in the droppings. I'm not familiar with which wormers treat which worms or the correct dosage and time frame for them. So it's possible a float *might* tell you something. But it also might not.
What I would do... get some electrolytes and probiotics in the water to combat the diarrhea. Or offer a little yogurt on the side.
I like Poultry Nutri drench... but there are a few other supplements that are supposed to be really good but haven't tried yet. I wouldn't use any vitamin to supplement during treatment with Corid since it work by acting as a thiamine blocker to starve out and slow the growth of cocci while the chickens own immune system learn to fight it off better. Make sure no other water sources are available.... also wonder how has your weather been since it can impact this.
I might just offer the egg scrambled. I wonder, since feed impact poo color if the syringed yolk had any effect? Being off feed definitely does.
Lots of homemade electrolyte recipes.. I use the first recipe, but with brown sugar...
https://104homestead.com/poultry-electrolytes/
They won't starve... but dehydration or electrolyte imbalance can be deadly.... not to be a fear monger.. just sharing.

I don't vaccinate either... don't want Marek's hiding on my flock. And cocci is irrelevant as a vaccination to me.
But I do think cocci is a possibility and would treat with the Corid.
Though it could be detected by a flock fecal float... and NO you might not have gotten rid of all the worms inside the birds. Round worms and tape are the only two that can be seen in droppings. All others stay in the intestine and only the oocysts (essentially microscopic eggs) will pass in the droppings. I'm not familiar with which wormers treat which worms or the correct dosage and time frame for them. So it's possible a float *might* tell you something. But it also might not.
What I would do... get some electrolytes and probiotics in the water to combat the diarrhea. Or offer a little yogurt on the side.
I like Poultry Nutri drench... but there are a few other supplements that are supposed to be really good but haven't tried yet. I wouldn't use any vitamin to supplement during treatment with Corid since it work by acting as a thiamine blocker to starve out and slow the growth of cocci while the chickens own immune system learn to fight it off better. Make sure no other water sources are available.... also wonder how has your weather been since it can impact this.
I might just offer the egg scrambled. I wonder, since feed impact poo color if the syringed yolk had any effect? Being off feed definitely does.
Lots of homemade electrolyte recipes.. I use the first recipe, but with brown sugar...
https://104homestead.com/poultry-electrolytes/
They won't starve... but dehydration or electrolyte imbalance can be deadly.... not to be a fear monger.. just sharing.