I use an alternate method of integration.
If you've got the space and materials, set up a "grow out" coop (can be a dog house or hutch) INSIDE the chicken run fence, and then use garden stakes and chicken wire or poultry fencing to make a little run around that coop. Give the youngsters their own waterer and feeder. Leave 'em in there for a week or two.
The older birds will check 'em out through the fencing but not be able to harm them. They can all see, hear, smell each other and even peck a little and do chest bumps through the poultry fencing without any injury to the youngsters.
Then just remove the poultry fencing and garden stakes, but keep the feeder and waterer there for the kids.
The big chickens will react to them like, "Oh, I know you, you're not a stranger. Just remember *I* get treats first, and don't get in my way. I'm senior."
There will be some pecking, some chasing, some squawking, but nothing serious.
Good luck, whatever method you use.