I don't think you need game swings until you find someone you trust and can work with. A good instuctor will have his own video and will be able to show it to your son after one session.
There are just way too many moving parts for your son to hit against high level pitching. There is a reason you hear the term "short to the ball, long through it" To be able to hit a high 80's FB on the hands and then wait for a change or a curveball you have to be short.
I will also say this you may end up with several instructors. My son worked very hard with a guy who was big on video, getting the "proper" mechanical swing, etc. They broke his swing down in the off season and worked on it for months.
He came back in his Jr season as was doing well, but something was missing. His scout ball instuctor was really in to timing and being loose and fluid. He worked with him on being fluid and not so mechnical and he exploded.
So be patient and work at it one thing at a time.