I know I've read some of your other threads but can't remember all the details. Giving those ages above helps some, thanks. A 15' x 15' run just isn't that big. I don't care if it meet or surpasses that magic 10 square feet per chicken in the run number you often see here, there is not enough room for them to avoid the two older hens enough when they hit the ground. Let me guess, when you go into the coop in the morning to let them out, the older ones are on the coop floor and the younger ones are on the roosts, avoiding the older. That's typical with mine when I'm integrating younger chicks.
You said the problem occurs when the chicks come down to the ground in the run. Things are fine when they are up out of reach. I'm a little surprised the chicks are in the run when the older ones are out there. It's not that unusual for mine to stay in the coop when the older ones are outside and I've got a lot more room than you.
When chickens have conflict the weaker usually runs away and things normally get peaceful though there may be a bit of chasing. They have decided who is the boss. If one cannot get away the winner does not realize they won and may keep attacking. If one gets trapped in a corner or against a fence and can't get away, they usually hunker down and try to protect heir head. The attacker often goes after the head, that's where they can do a lot of damage. When this happens it is a dangerous situation, chickens can die.
It sounds like you have two older pullets that are brutes since they seem to go out of their way to attack the younger. That happens but there is some bad luck in that. Them still being pullets themselves may contribute some to that. I don't think my hens would go that much out of their way to attack them in the conditions you describe.
Is one of your feeding and watering stations inside the coop? That might let them eat and drink without being attacked. They may spend all day in the coop if you do this.
You can try putting some type of platform up high with food and water. That way they can eat and drink without getting to ground level where they will be attacked.
Other than adding more room or keeping them separated until they all mature some more I can't come up with anything else.
I wish you luck.