Good looking rifle. Estimated price range looks appropriate for an 8x51. Suspect somewhere in the middle to low middle should be the hammer price, but ya never know.
8x51 - strictly a handloading proposition here, making the cases, special dies - maybe. Might be able to use a shortened 8x57 die. Could be .318 groove dia. I suppose.
This was off a search:

Edit: As Springfield Armory and some American makers were quick to steal ideas from the Germans I wouldn't be surprised if the 308 was simply a continuation of that practice as the 8 X 51 preceded the 308 by about 20 years. I believe the 8 X 51 could be made by quite simply necking up the 308 to 338, set a false shoulder to set the headspace and neck to 8mm, then fireform. The 8 X 51 SHOULD be .323 but as that's a sporting rifle the bore needs to be slugged to make certain. Even though .323 was adopted by the German military in 1905, 8mm sporting rifles in .318 were made right up to the start of WWII.

Of course, this nekcing maneuver on a .308 depends on the shoulder dia. of the 8x51.
If it is tapered like the 7 and 8mm Mausers, then perhaps one of those dies could be used to reduce the shoulder sufficiently.