Good Points here so far. Getting the right hand on the rope is good and good training to take the 5 to 7.
I would also add that he is taking his head out of the spin early, he is spotting his landing at 360, this is causing his hips to stop rotating. The lack of hip rotating is why he is muscling around the spin so much. If you can get you head, shoulders, and hips into a spin you money. If you look at the vids his head and shoulders are spinning faster than his hips once he gets the 360 mark, that's because he is spotting his landing early. I had this problem going from TS 540 to TS 720. You have to think about the 540 as a 540 not a 360 with another 180 at the end, this will help loads. Tell him to try and just jump onthe ground (not the water) and do a 540, if you spot your landing at 360 jumping on the ground your rotation is done instantly. This will force him to think 540 instead of 360, all he needs to do then is apply this rotation to the water. I hpe this helps and makes sense. When I was learning ts 7s I would spot my landing at 540 then try and muscle the last 180 around. Finally a buddy of mine who is a pro snowboarder, pointed that out to me and said keep your head in the spin, think 720 not 540+180. I landed the next one i tried!
Good luck, post some videos of him stomping that thing.