I would say you are right that the 3 better looking ones are the picking culprits.
Sometimes even with a lot of space you can have issues. More protein in the diet can sometimes be helpful as well, so if you are only feeding a 16% poultry feed, try an 18-20% all flock feed.
That's the way it is a lot of times - you can read wonderful stories/blogs, etc. about chickens and the writer paints a lovely picture/description. Happy, sweet tempered, fluffy bottom hens just sauntering joyfully through the yard. Well. They don't tell you that hens are quite jealous of one another and can sometimes be plain downright nasty with each other. I've had some mean ones and I've had some very sweet ones. It is what it is, but downsizing/culling is sometimes a solution to those meanies. I've not done it that often, but I've found that removing a hen or a rooster can often bring a lot of peace within a flock.
You are doing fine. Do the best you can.