I have had success with a male an female APBT living in the same house and not having to rotate them when we were home. We just had to be careful when high valued treats were around. We couldnt play ball with them together or a fight would break out. You just have to know what triggers your individual dogs and manage accordingly. I think its a good sign that your female has not had aggression issues yet, it might also help if you got a male puppy from a litter that was more bully or am staff and further away from game lines. These are all just ideas, but only time will tell. It is always a gamble but i can be done.
If you own any variation of the breed, mix or otherwise, you have to expect to put forth the effort to be PROACTIVE and stop a fight before it starts. It's called being responsible. If you openly say you don't want to crate and rotate.. you probably should not be bringing yet another puppy into the mix. You also seem to be really talking bloodlines up a storm..when all you own are mixed. How do you KNOW if what you already have is/isn't gamey? How do you plan to choose a pup accordingly? Any mix you bring home, like what you already have, may or may not be gamey. No one will ever know with no papers. Do what you will. But be prepared to be PROACTIVE. If you think that's an inconvenience.. then be happy with what you have.