Not at all hard to find 10/22's. The thing is if you want to build one with a short overall length, you need to start with a bare reciever. In Canada, you can only cut down the barrel to 18 inches, and reduce the OAL to 26 inches. Go any less, and it might as well be a machine gun. HOWEVER, if you import a virgin reciever, and register it as a restricted firearm (like a handgun) than the other rules don't apply. The barrel can be any length you want and the gun can be as short as you like.
Only problem is then you are restricted to only taking it to the range. In my case, I do 95% of all my shooting at my club, so it doesn't matter.
Right up until we loose all our handguns after this next election.