Hi Erich1980,
While not a true expert I have been doing a huge amount of research about anthias in general and Dispar (among a few) in particular. Wrott has a very good point. It's not only about aggression. It's about the comfort the fish feel. In the wild anthias school in the water column very close to large coral heads with loads of hiding places, including between the branches of coral. In the photos I have seen the fish are usually beside the hiding areas, not above. Your tank, beautiful and healthy, has densely packed corals on the bottom, with free swimming room above populated by several large and extremely active fish. I think I saw 4 good sized tanks, one of which looked like a salad plate. So behaviorally the only place to hide is on the bottom, behind rock, which is where most are. Despite no aggression, the anthias likely perceive the space above the coral as very dangerous. So I guess what I am suggesting is that if you want to keep these fish some new landscaping might be helpful.
Good luck with them!