The rules in The Stack are totally different from the "little kid" programs. No wrist bands, no sign in or out rules, etc.
As to a 13 year old moving down--that is sometimes allowed. However, it is not allowed for a kid to go back and forth between programs. That is, he'd have to be registered in one or the other. They are quite strict about not allowing a 12 year old in the Stack (unless within 30 days of 13th birthday). When DD was 12, she thought this was "mean," but after she turned 13 and I saw the set up, I feel it is really for the best. Remember that there's a huge difference between a "new 13" and a 17 year old.
I'd suggest that you talk with the counsellors--they do occasionally make exceptions. In addition, there are lots of places/things the kids can do outside of the programming so that they can attend their own programs when desired and "hang together" other times. ALternative activities include sports on deck 9, the pools and eateries on 9, movies, and anything listed on the navigator as a "family" activity--karoke, building the vege racers, games, etc.