Since it was introduced in 2004, you might want to call Remington and talk to them directly about it before changing anything. I would think it'd still be under warranty at this point. They might have you send the rifle back & stick a new barrel on it themselves. They'll definitely test the living daylights out of it.
Cold barrel shouldn't be THAT far off...
Check the bedding (or lack thereof).
Checking to see if the stock is slightly cracked/warped/etc at mounting screw points would be the next thing to do.
Check scope, mounts, & rings
Might be time to pillar bed the action & float the barrel before going to all the trouble to Cryo it...it's less expensive. And fairly easy, just time-consuming.
The current price for One Cryo ( One Cryo Cryogenic Gun Barrel Tempering for Increased Accuracy
) is $45 plus $10 return shipping plus whatever you pay the local gunsmith to take it off & ship it ($60) if you don't do it yourself.
Other options include purchasing a new barrel...
Waitaminit, just thought of something else....you aren't using Remington Golden .22lr ammo, are you??? That stuff is spotty even through Rail Gun.