Sounds like your cat run is a great place. The cats are safe and they can do the things that are part of being a territorial predator without harming their human's home. Some cats "get" human rules and some just don't. It sounds like the best possible compromise. It is hard that he cries for inside time, but his behavior inside was "crying" for freedom to be free to act out his needs too. In my opinion you have given him a really great gift.