I think that I would need, for my own sanity, to cut him and his family loose. The fact that mom calls him a "free spirit" to lighten the seriousness of his behaviour tells me that no matter what you do or say, he will be allowed to do whatever else he wants to do at home.
I am not saying that kids with lots of energy are the problem. When that energy is channeled correctly, you end up with the most precocious, bright and happy kids around. When it is not.... you end up with what you have on your hands.
In the meantime, I would just get hard-butt on him. When it is quiet time, we are QUIET. If that means that he is sequestered in a room with books and puzzles by himself, because he is unable to control himself around the other children; so be it. No wrestling, means NO WRESTLING. What is a consequence that will impact him? For one of my little guys, it's not being able to play with other kids. So if he is not respecting our guidelines, then he is my shadow for the day. He doesn't play with the others and quite literally has to be where I am for the remainder of the day. It is not fun for me, admittedly. But I also don't "entertain" him for that time either, so it's definitely not fun for him. He smartens up pretty quick....
And on another note; make sure you are telling him EXACTLY why he is being reprimanded this way. He is old enough to understand, for sure.