This does sound like a good start. Remember that often in cat groups or even in pairs, they do establish dominant and submissive. So some "discussion" among the cats about who is going to be dominant is okay. I would only worry about refereeing if it gets too far out of hand. It is good that they have their own rooms for breaks. Just keep letting them be together for short periods of time. Gradually increase that time. It sounds like you will likely have a pretty good transition. There could be minor setbacks but overall, it sounds like these cats might ultimately be friends.