Looks like a normal lesion/peck wound to me. I have had this with roosters, they get a small cut or scrape, then as it scabs over they stand there and let the hens pick at it making it worse

I would try Nu Stock or Pine Tar - either of those are supposed to taste bad and deter picking. If mine got bad enough, I separated my rooster out for a while until it healed.
It would be good if your vet could do a fecal float then - this will let you know if worms may be a problem. Since you are having trouble with wet ground then worms and/or Coccidiosis may be at play too.
Darkening of the back of the comb could be a number of things - from heat stress, dehydration, hormones to reduction of oxygen/organ dysfunction.
I'm sure it has been frustrating for you to rely on someone else to help out. Your own health is important, so just do the best you can.
To help keep water bowls cleaner, place them on a cinder block or something else raising them off the ground. I even have a few bowls on old lawnmower tires, they fit perfectly.
My bowls do get dirty and sometimes I have to actually clean them out a couple of times a day depending on how much straw gets kicked into them.
Straw is another useful idea that was suggested. It can get mucky so if you see that as a potential problem - get some bales and leave them intact. Place the bales inside your run so the birds can get on top of them - this allows feet to dry out and mine love to get on top of straw bales and scratch around. Eventually they do start to break the bales loose and then the straw just gets scattered around the run.
Just for reference, I'll show you my feed cups for the layer flock. I usually keep 4 with feed and 1 with oyster shell. Having more than one "station" keeps squabbling down.
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