I integrated my flock in the coop/run about 3 weeks ago. My girls are the same age as yours. The "big girls" Junebug(barred rock) and Gertie (Americauna) are 16 weeks. The "little girls" Buttercup (buff americauna) and Daisy (RIR) are 8weeks.
In the morning I put the little girls in a wire puppy crate inside the run, the big girls were able to examine them from all sides including the top. I only let them have access to eachother when I was there to supervise. I really didn't interfere unless the big girls started to get mean and then my foot or hand as a barrier seemed to calm them down. I did that for probably at least 2 weeks. Also I fed a lot of treats to the girls, I know this is probably bad but it seemed the more treats they had the less they focused on the new girls. So I fed them as much cantaloupe/fresh corn/ melon as they wanted until the frenzy was over and everybody calmed down. With full bellies they seemed much more docile
I have to say that although the big girls tolerate the little girls and there is not much drama in the coop now, I have two pairs of hens. The big girls roost/ lay in the dirt/ eat together and the little girls do the same. Rarely are all four together, unless its treat time
One difference I did notice is my run is about two times bigger than the picture I saw of yours. The little girls are able to give the big girls plenty of space, there is lots of room for them to run away.
In the morning I put the little girls in a wire puppy crate inside the run, the big girls were able to examine them from all sides including the top. I only let them have access to eachother when I was there to supervise. I really didn't interfere unless the big girls started to get mean and then my foot or hand as a barrier seemed to calm them down. I did that for probably at least 2 weeks. Also I fed a lot of treats to the girls, I know this is probably bad but it seemed the more treats they had the less they focused on the new girls. So I fed them as much cantaloupe/fresh corn/ melon as they wanted until the frenzy was over and everybody calmed down. With full bellies they seemed much more docile

I have to say that although the big girls tolerate the little girls and there is not much drama in the coop now, I have two pairs of hens. The big girls roost/ lay in the dirt/ eat together and the little girls do the same. Rarely are all four together, unless its treat time

One difference I did notice is my run is about two times bigger than the picture I saw of yours. The little girls are able to give the big girls plenty of space, there is lots of room for them to run away.