Quoth James K:
The only real drawback to 8x57 is that the bullet selection is not as great as with .30 caliber and lightweight bullets (like the 110 grain .30 caliber) are not made. But otherwise there is nothing the .30-'06 will do that the 8mm will not do as well or better.
This, pretty much.
The biggest drawback I see to the 8x57 is that factory ammo might be a little tricky to find, depending on where you shop (don't think I've ever seen it in chain department stores, for instance). If you handload, though, the Mauser round is at least as versatile as the ought-six and arguably more efficient.
125 grains is about as light as you'll find in .323, but you might consider going with cast bullets and just loading them for lower velocities. A lot of people seem to like Trail Boss for reduced loadings in the 8x57.
Otherwise, yeah, something in the .308 Winchester (*x51mm) family would be a good bet; those rounds are almost functionally identical to the 06 family and should cycle just fine from a 98 magazine.