You are separating the wrong birds. Put the bullies where you have her. Adding a single bird is a tougher integration, but you are almost there.
Go in tonight in the dark, pull the two meanest birds off the nest, and put them in the crate. If you have another space, like the garage - put them there. Leave them separate for a couple of days or a week.
So if I have the count right, that leaves two bird, I would put those two birds out in the yard. Now let the new bird in the coop/run. She can now explore around, eat, find escapes without being chased for her life. If you can feed along the fence line that often works too.
Then late in the day, let in one of the other birds. One on one, is a whole different game than 4 against one. There might be a bit of bluster, but let them work it out if you can. Take a squirt gun, or a water hose, and squirt both of them if they get into it. If it is truly terrible, try a different bird, but I don't think it will be.
After 2-3 hours, just as it is getting dark, let in the third bird. The urge to roost is nearly as strong as the urge to fight. Just watch with the hose handy, but I am expecting all those birds to get into the coop and roost. Call that good. If the new bird does not roost, but gets in the coop, that is enough.
If she doesn't, but returns to her coop, I would not fret that either. Now, I would let this trio have the whole set up for several days. Then I would add one of the two in the garage. There might be a dust up or two, but should settle, a day or two later, add the other.
If two or more of the birds are heartless, you can also use pin-less peepers. I would be strongly tempted to put these on the two in the garage. They can really help with aggressive birds, in smaller confinements.
I think this will go, but it will take some fiddling around. Did you add the clutter?
Mrs K