I have turkeys, but they don't fight. I have one is trying hard to mate a particular hen, but she's having none of it.
When my CHICKENS fight, I never allow more than one on one, face to face. Meaning don't bother cornering anyone. Don't bother with ganging up on anyone. I'll break it up. I'll put you in time out. (It's very rare that they will do that.)
If one is injured, I look to see the source of the blood. Most of the time, I just wipe the blood away. If the blood is pouring out, then I leave it be. Many people put something on the owie - blue kote, neospirin, and stuff like that.
I have only wrapped one owie on a cockerel - his spur was nearly ripped off. I cleaned it, wrapped it. Bandages stayed on for a week, then I took it off. The spur healed.
I have wrapped one owie on a hen - after doing surgery on her foot. Rebandaged it once, and now you can't tell she ever had a limp.
If it were me, I'd keep the group separated. If the one turkey got outside, let him be. Maybe take him in after everyone has gone to sleep. Maybe give him a place to be during the day where he is not in danger from the other guys.
Move a friend or two out with him.
You said you didn't have a separate place to keep him. How about subdividing the coop? Putting up a sheet or something?
How about the same for the run? Subdivide it with something a visual divider or even a make shift fence from chicken wire or hardware cloth.