1. Can a 338-06 be rebored to 9.3X62 (an old Shaw 24" 2 1/2 contour barrel).

2. How about a M77 (round top tanger) be rebored to 338-06?

With few exceptions, it's usually quicker and more cost effective to rebarrel a boltgun. Reboring rifles is best for barrels that require a lot of machine work or if you want to preserve the outer appearance.