If the barrel is in good condition, save your money and keep the 8x57. Use the saved money to buy good reloading equipment to reload for the cartridge as there isn't much choice out there for usable factory loads. Handloaded, the 8x57 will pretty much equal the 30-06 but with a larger diameter bullet- kind of a halfway point between a 30-06 and a 35 Whelen. In fact a 338-06 isn't much of a change from the 8mm other than the fact that you can shoot heavier bullets yet.

If you already have a CZ-29 you would want to reload for that one too. You can get amazing accuracy out of one of those rifles. One of the best bolt action rifles ever made IMHO.

Alcohol, Tobacco, and Firearms... who's bringing the chips?