@Cycloptichorn,
If your son did well in a Montessori school before, and you've found another one you like, which you feel will provide a stimulating atmosphere for him, what is your hesitancy about enrolling him there? Why did you take him out of the first Montessori school?
Will it be disruptive to him socially to move him to a new Montessori school? Does he have friends in his current public school he might not want to leave?
Have you taken your son to visit the new Montessori school? If so, did he seem to like it? If not, perhaps you should take him to visit the school, and include him in your decision.
AP classes in public schools have routines and structure, with limited freedom of choice. The academic work is presented on a higher level, and, in that sense, it is more challenging. But the format isn't significantly different than it is in the regular classes.
I don't think it might be good to keep moving your son around to different school environments over the long haul. If I understand you correctly, it sounds like he's been moved around quite a bit--public school, Montessori, home schooling. That might make it difficult for him because he's always adapting to different learning situations, different routines, and different social environments connected with school. Choose what you think is the best learning environment for him, and then try to keep him in it, at least for several years. Help him learn how to cope with boredom, it's something he'll need to know, no matter what kind of situation he's in, because one can't always have complete freedom of choice to alter the external situation.