Adding new chickens will change the entire flock dynamic and they have to start from scratch trying to decide who belongs where, and the top hen will likely be the most aggressive to keep her place. The easiest transition occurs when you use the
See But Don’t Touch method. That's keeping them separated with some sort of fencing for a week or 2, so they can still see each other without being able to cause damage. Putting feeders on each side of the barrier will also help them get used to eating together too. Free range time together also helps because there's lots of room to run away.
Skipping the separation step could prolong the pecking and even enable fighting to continue until someone is terribly injured. Throwing unfamiliar chickens in together is more than just a pecking order establishment, it can be a war. These are intruders that are not welcome and are a threat to their food supply and home, and the existing birds will try to do whatever it takes to get rid of the intruders. An injured bird MUST be separated right away because the sight of blood can cause a frenzy of pecking, even by her friends, and could easily lead to death. After being introduced properly, there still may be some pecking, but that's normal.
Some people have added chickens without too much concern, but in your case, the original RIR are typically more dominant than the docile BR and BO, and it's not in newbies' favor.
There's many reasons chickens stop laying: less daylight, predator invasion, parasites or illness, a change in surroundings, new location or routine as well as the stress of fighting a war. Separate your groups of birds, let them get used to each other peacefully, and they'll start laying again.
A rooster will not quicken the process.