I chucked my heated plate when it couldn't keep up. I bought this for my flock:
Farm Innovators 6 qt. Round Heated Plastic Pet Bowl, P-60B at Tractor Supply Co...
It sounds like they're also in their hormonal teenage girl phase. They should calm down once their hormones settle a bit, but just incase, keep the spray bottle at your belt. 😂
I don't have biting hens, but I have 2 roosters occasionally bite me. I say occasionally cuz they don't try for me much since I started spraying their heads with cold water. I wouldn't do it when it's cold out, but the rest of the year I suggest trying cold water loaded in a spray bottle or...