My Vote: 7X57!
The 7mm Mauser is my favorite HP rifle round, only slightly ahead of the 6.5 Swede (X55mm).
One advantage of the 7mm is that you won't have to modify the bolt face or magazine, as the 7 shares the same length (57mm) as the original 8mm.
If you reload, as you should if you want to realize the full potential of the old 7 (commercial loadings tend to be loaded on the light side to allow for old Spanish 93s and rolling blocks still floating around) you can resize brass from plentiful .30-06 or 8mm casings. Might have to turn the necks a little; might not.
The 7 will do anything that a .308 will do, without kicking you bowlegged doing it.
If you have the M38 small ring action, the Swede 6.5 barrel might be easier to come by, but surplus 7mm M95 barrels might be available too - keep an eye on the auction sites.
I have a 38 K KALE that I have considered rebarreling to .308, and if I find a good deal on a small ring barrel I might do it.
Have already made a .308 carbine out of a battle weary 24/47.
I think that we both like to tinker about as much as we like to shoot!