I usually start by letting the young ones hang out in the coop during the day for a couple of days than I make them a separate pen in it for another week or so until I feel comfortable with all interactions, then they are on their own except for being rounded up in the evening if necessary.
I have been integrating chicks for 20 years. Older birds, anything older than three months always had a rough time. I too stumbled on it and was surprised how little the older birds bothered the chicks. Later when I had a broody hatch and raise chicks in the flock I noticed no one bothered those...
It's easy to integrate young chicks to a flock because it's normal and not a threat. They assume they are someone's chicks. Older birds are seen as intruders. I let my adult birds see my 6-8 week chicks for about a week than I let them out. There's an occasional peck but just like you've seen...