lol it does take time, I'm going to have to do the same thing here soon, but it's harder in a back yard. most of you all have land, I got a back yard. It was not bad dealing with integration, but two hens refused and so I took them to moms, she had them over the summer and when I brought them back home I figured they would be low on the totem pole, nope they took right after them and would not stop, even drawing blood. Making the other chickens constantly running also. They went to a new home. I just rather have a broody, they do all the work and I can be free to just let mom raise and integrate. Makes life a whole lot easier. Now today I got another broody, anyone got eggs for me to put under her and Iive close lol.Just adding my experience in integrating chickens. I found that it is better to integrate three or more at a time rather than just one. I currently have a mixed flock of bantam and LF chickens that live in the coop together without issue.
I have a large fenced area for chickens to safely play. I also let everyone out on nice days to wander the acre.
I bought a large insulated home-built dog house that was on craig's list and put it in the corner of the fenced area. When my bantams were about 5-12 weeks old, I put them in the dog house and left it open during the day in the large fenced area. The little ones could run into their own place if frightened, and there is a lot of room in the pen to get away from the large chickens.
They integrated very well in this setting. I would say it took about a month of slowing intermingling on their own to become comfortable with everyone in the pen. They all get along fine now despite size.
Now I am integrating them into the coop a few at a time. Never less than 3. It takes time for the bigger girls and boys to accept the new ones into the coop. If they start to pick on just one of them, I take it out and put it back in the dog house and put a different one in it's place in the coop with the other two that I am integrating. So far this has worked. I hope it keeps working because I have another 2 batches that will have to integrate the same way.
As long as I don't crowd them, there appears to be no problem.