Does your flock free range?
I let the existing flock out for a free range while the newbies are locked in the coop and run. This gives the newbies the opportunity to explore and feel comfortable in what will be their new home without the threat of being picked on and also learn where all the good hiding spots are.
Same with free range, but reversed; I let the newbies wander around the garden while the existing flock are locked in. Granted, the existing flock have a good whinge about this

but again, it gives the newbies chance to explore, get settled and find all the good hiding spots without being picked on.
I find that free ranging is a good opportunity to let everyone get to know each other .. space is a great tool when integrating.
I also find that a water pistol comes in handy .. it is amazing how a squirt of water in front of them can cause a chicken to change her mind about picking on someone
There will probably still be bickering while the pecking order reestablishes itself when they are integrated, but it should not be quite as brutal.
Also, when they are integrated into the run and coop, for a couple of months I ensure that there is more than one source of water and food, just in case the newbies are being bullied away from either.