CAUTION here! Rebarreling a pre-war Mannlicher-Schoenauer is no big problem, as the cams which push back the locking lugs on opening to achieve initial extraction were machined inside the receiver ring. Post-war models, at least the 1952, had these cams machined as part of the barrel! This simplified production at the factory, where special tooling and fixtures were available, but it is nearly impossible for a normal gunsmith to get the barrel threads and those camming surfaces correctly shaped and aligned. I know a very good master gunsmith who told me he did it once, but would rather close shop than do it again.
Reboring to a larger caliber is not such a big problem, despite the necessary alterations to the magazine. So before damaging the original barrel, have it unscrewed carefully to check the arrangement of thos cams on a 1950.
BTW magazine aleration may be necessary for the change to 6.5x65 too, as the base to shoulder dimension, 2.12", is longer than that of the .30-06, 1.948". At least the guide ring as to be altered, and maybe even the rotor. So before starting the rebarreling get 5 6.5x65 cartridges and try if they fit into the magazine.