If your .222 bullets are indeed "tumbling" as in very poor accuracy at all distances, and verified sideways impacts on paper targets, the first place to check is the muzzle crown. If it is damaged, you will never get any respectable accuracy. The gunsnmith should have checked this first.
Secondly, if you handload ammunition, make sure that you use .224" diameter bullets. Bullets are available a couple thousandsths smaller for the .22 Hornet that will give terrible accuracy in the .222 Remington.
Third, as for the barrel being "shot out"... that is HIGHLY unlikely in a single-shot .222 Remington rifle. The caliber is famous for phenomenal barrel life, and as a singleshot, it would almost impossible to fire it fast enough to overheat the barrel.
Take it to a REAL gunsmith for a second opinion.
John