Good point Jerry.
He's a built 7 year old with short arms.
He's been steadily scoring 950+ in youth air-rifle competitions supported. Good habits, and patience to score well.
His experience with 22 stops at 150m with a scope.
Congrats on your sons solid groundings... can't buy patience and a steady hand... which can only improve with time and practise.
Weigh his air rifle... get him to pick it up from the wrist/grip area and move it around. Many PRS rigs are set up when the rifle is ON the bag and little thought goes into moving it TO the bag. Unfortunately, loss time and possible damage happens as the shooters struggles to transition between positions.
Get all the buttstock dimensions off this rifle IF he is comfy in typical PRS odd ball positions... adjust LOP, comb height and then compare to commercial stocks/chassis. The overall length of the rifle is also important to figure out. Having a musket as long as he is tall means he isn't going to be able to pull the rifle out of a prop without a few steps backwards.
My guess, there is nothing that will suit. I would strongly recommend AGAINST a chassis as the total mass of the rifle will be too heavy for his current strength (guessing at this point).
I would strongly recommend you look at a 10/22, modified hunting stock (AR grips and ergos suit larger hands), flush factory mags, 'tactical' contour steel barrel.. maybe HB but shorter then the norm.
It all boils down to how much weight your son can move comfortably AND safely. ALL popular bolt rifles have a mag that hangs out the bottom. This forces the rifle to rest on the forend AND that demands alot of front weight to help with balance. Odds are the weight of the ballast is more then he can carry.
With a 10/22, you can use the trigger guard as the rear brace. This massively changes the balance point allowing a far lighter rifle to be used and still balance. Kids will naturally take longer to find the scope and target. He gains time back because he is not running a bolt, disrupting his sight picture. Being in the scope when he fires, he has a higher chance of seeing his hit/miss and adjusting quickly with a second shot.
Activating the safety with small fingers is far easier then trying to control a bolt that wants to slide back and forth.
PRS is a time management game so let's give me as much working time as possible.
Happy to help you set up this rifle.. pm or email to discuss more.
Jerry