I hate to be the guy to pee all over someone elses parade but you do know there are
M1 carbine stocks available for the 10/22 already right?
don't get me wrong, the tech sights and handguard do give of the M1 carbine vibe but the 10/22 stock just doesn't have the same profile and the ruger stock ring doesn'tfit around the hand guard to lock it in place so it's a little less convincing of a conversion. the JB weld on 10 rounders is a good idea though, shows quite a bit of ingenuity on your part.
I'm lazy though, I'd rather just buy the $100 conversion stock and tube of plastic weld and call it a day.