Mine pass through a similar door and their tail feathers are not getting broken. Their tail feathers do get worn and broken during spats. Yours are at the age that they should be have pecking order disagreements.
I don't recommend husing poultry wire around turkeys. I have seen tom turkeys...
As long as you keep multiple toms together, they will always have broken tail feathers. The broken feathers will only be replaced when the bird molts or if the feathers get pulled out.