OK, so it is the "most hardest to right of all" whatever that means-- so tell me exactly how you have actually accomplished a shrink fit of a 8mm liner (or similar size) in a .22 cal rim fire rifle. Are you speaking theory or actual practice as I would like to know as I don't how you can get the bore for the 8mm insert within the same diameter +/- .001" for the full length of the barrel, without using the same type equipment that rifle barrel manufactures use to bore a barrel blank. Not to mention how you heat the barrel and hold the temperature while you somehow force a very long chilled tube down the heated barrel (for maybe 22 inches) without the tube seizing after about 4 inches of travel.
I have been repairing and restoring rifles and shotguns for 40 years and even though I don't believe the shrink fit you mention is possible in a gunsmiths shop, I am always open to learn new methods.
Best Regards;
Jock