I agree... while I feel that my 10/22 is my favorite gun of all time, to try to upgrade one to be a competition winner would be a long haul... That's kinda like those kids you see in the hopped up hondas that they spent thousands on upgrading... Buy a decent used porsche and you're already there is my mantra... If you start with a high quality best of the best platform, and tweak it as needed you'll end up with something truly top of the line for the same amount or less than tricking out your grandma's old civic.
Seriously though, the 10/22 is my favorite gun but my old bronco is my favorite car. It won't be winning any offroad competitions, and to make it do so I could just purchase a military grade humvee.
The money spent on triggers, barrel, stock, getting the action worked, putting a high end scope on it will all add up to over a thousand bucks easy... Now, that said. This is like the old rodeo saying, 'it ain't what you pull up in, but what you pull out of it" so if you've got a pretty sweet shooting 10/22 already and are a fine shot with it, take it in there bone stock and kick their butts with a $200 dollar gun, I guess it would depend on how good the shooters are in your club.