There was a guy (from Australia ?) who did just that - how to get better groups from Ruger 10-22 - for cheap - layers of foil tape along each side at rear - inside the stock - to eliminate side-to-side slop; a few wraps of electricians vinyl tape around barrel to create a "bedding point" and to centre the barrel in the forearm, while also giving "up" pressure on that barrel for the V-clamp attachment; filed out underside of the barrel band so that there was no contact with the barrel. I do not recall if he did anything with the trigger at all. I did all three of the mods listed. If I remember correctly was total of 13 layers of foil tape to eliminate that receiver slop - 6 layers one side and 7 layers the other side - receiver is now a snug, just barely, sliding fit, back into the factory stock. That one has an aperture rear sight - my main "cheap" learner rifle to try to learn to use that sort of sight.
Reflecting on what he came up with, Ruger 10-22 from factory has one action screw to hold barrelled receiver to stock - so left/ right slop at rear of receiver is only to be controlled by the fit to that stock, there. The V-clamp on the barrel is to the bottom, I think - so the tape wrap is helping to counter-act that pull? And filing out the barrel band just makes the barrel like "free" to do what it wants in the air. I think. I am not really good enough with aperture sight to prove those made it more accurate or not - would not have been the first afternoon spent at "busy work"...
FYI - my 10-22 was bought new by me in late 1970's - the older carbine styling. Without dismantling for accurate measuring, I would say this barrel is about 18.5". For some years, it wore a heavy barrel and was in a "target" type stock bought in a clam shell "kit" at Canadian Tire - with scope, I do not think that improved much, at all - is now back with original barrel, but the stock is a NOS, not the original. Not certain that barrel length, per se, has much to do with "accurate" or not. At least on this one, the barrel tenon is a smooth shank, barrel more or less slides into the hole in receiver held in with a V-clamp - so to "screw in" another barrel would need fussy alignment, then perhaps precision drill or ream, and then tap or internal threading, to get some threads into that receiver. Would be way over my head to try that.