Suggestions:
Do you not have an AR? They're plenty ambi and the stock adjusts. .223 works, it's just a little sub-par on leaving a blood trail sometimes. A barrel and bolt change gets you into 6.5 Grendel. I would suggest the bolt and barrel from 65grendel.com group buys.
Lead wool in the butt will soak up recoil, but that's the worst place to add weight for a youngster if the rear is not supported during shooting.
A Lee hand press, dies and scoops are fairly inexpensive. A neck sizer die is easier to deal with on the hand press. You only need to get it going fast enough to open a 120gr Ballistic Tip. Slow loads tend to group well.
AND, if the kid only ever fires the 7mm08 at deer, having done all practice with 22lr you might not have to do any of this anyway. That's what I do. These kids don't know their ARs have any recoil. To tell it all, a 22lr AR does have the big bolt knocking around, so it moves somewhat like simulated recoil, but I really don't think they notice the recoil from the lighter centerfire rounds when fired at deer.
