In my opinion poor/worn out barrels produce bad groups, but not flyers. Poor rings and scopes produce bad groups, but rarely result in consistent flyers. Consistency of flyers is almost always a product of poor bedding, sticky trigger, bind in the ammo box, or poor torque as rudysts mentioned. Good chance it's a combination of those.
My suggestion would be to have a good smith check the barrel. No sense in trying to solve a flyer problem if the barrel will never produce groups. If the barrel is ok then start the process to eliminate binding in the action and/or box.
If it's the lightweight barrel model, don't be afraid to start off with a neutral full length bed. Two of my top three shooters were mediocre shooting lightweights until I full length bed the barrel. The Kimber went from a 3" gun to a 1/2 inch gun after doing nothing more than full bed and eliminating a box bind.
On a separate note: I shoot a lot of Core-Lokts and a lot of 7mm. I have yet to own a 7mm that likes the Remington 175 grain Core-Lokt. Never experienced flyer problems with it though.