Hi there! I'm offering a fresh perspective on this. I use the gradual integration approach but my hubby also heard from a video of old Maltese man that they sprinkle baby powder onto all the chicken tails and backs while perched at night. Then they slip the equally sprinkled newbies in. So I tried it, as follows.
My rooster needed additional girls as he came of age. He only had one in his (big) cage. They were familiar through the fence only. I powdered them all up and slipped 2 relatively new hens on the perch Friday night. The next morning (yesterday) there was not a single squabble or sound at dawn, or after, as they seamlessly integrated!! My theory is that it works as a distraction. They are so busy preening the strange powder off, that they forgot to fight! They even shared at feeding time. So for the moment I think the combined approach could be ideal. I even got the very first egg of the season from the introduced older hen, today (Sunday). She's only been in the new coop with the new flock and roo, for one day! Very happy with the integration. Was like a dream.