Alibiiv, I know you want to get a killer barrel and all, and I just took a look at your other thread.
The heart of AR's is actually the upper. The lower just houses the fire control group and magazine.
If he wants to shoot tight groups changing the barrel on that M&P will be a start but as noted there are many other factors to getting a truly accurate AR.
Everyone loves a build project and maybe that is really what he wants to do, but if he wants to have a gun that just works and shoots tight groups, read on.
One person on that earlier thread mentioned White Oak Armament. These guys specialize in competition uppers. For $600ish you can buy a complete upper. Slap a decent trigger in that lower and he will have essentially two guns - the original M&P and the complete white oak upper that shoots bugholes. Two pins are all it takes to swap uppers back and forth.
The big stainless barrels aren't even threaded. The uppers are 223 Wylde chambered, sorted out for accuracy guys, and they will shoot. Take a look I know it's not the direction you were headed but honestly you're wasting money on that Proof and gas block.
They make Varmint type uppers with longer barrels. If he truly isn't going past 300 a 16" 1-7 barrel is great and will be waaaaay less awkward and heavy.
Take a look at the SPR type uppers.
Link to White Oak SPR Uppers Page.
If I were buying one today I'd get the SPR 18", rifle length gas system. It would shoot verrrrrry soft. Your son also might like the 16" midlength gas system. the SPR uppers have a lighter contour and are threaded on the end. I would want to run a suppressor so SPR would be what I'd pick.
The other type, unthreaded with heavy barrel will be something more like this.
Link to White Oak Varmint/Predator Uppers
Look over their website they sell a ton of competition specific uppers.
And know that M193 ammo (the 55 grain stuff most people buy/shoot) is not going to group well.
(Full disclosure I don't own a White Oak, but people who know recommend them highly. I have an old Rock River varmint style AR 16" that shoots as accurately as I care to fool with in AR's).