I was going to hop in here, but
@3KillerBs is giving first class advice, and very personal attention.
As has been observed by others, your coop is much better than most we see from first time owners, and the hawk means nothing but covered runs for you. Birds can be integrated at that age, I also use the see and be seen method (my Sig is in the flock below). I am currently integrating ducks (now age 4.5 weeks) they've been at it for more than a week, and have successfully integrated both my prior chicken hatchings (now roughly 8 weeks and 11 weeks) into my adult flock. Its not instant, but the method works.
The last thing I'll add, and the only thing "new". When you increase your run, make it wider. Space is a social lubricant (so is abundance - multiple feed and water stations are your friend) - your current run is a little tight on square footage, but its not catastrophic. OTOH, its narrow enough that one bully hen can dominate the run - no space to get around her. Doubling or tripling the width will not only address the space shortages, but will make it so that no single bird can control the whole space. "Pecking" order will still occur, of course - but the chances of more injury than a few missing feathers and comb pecks will go down dramatically.
Oh, and throw some obstacles in there - if you have any of those paper thin plastic "pots" you get large shrubs/small trees in? They work great. So do 5 gallon buckets. and take the extra 5' roosting bar out, install it in the run somewhere. When the weather is nice, your birds may want to stay out, and again, its enrichment in the run space. Bored birds often create behavior problems. Like bored children.