Great gun and the 8x57 is a great caliber. You need to look at the proof marks carefully and/or slug the barrel. If an early gun like you first thought (I agree that it looks like a post war gun) then it is likely a .318 8x57JR. If post war, it may well be an .323 8x57R. This matters (a lot) so make sure you know before launching a round down range.
I hunt an 8x57JR drilling often, and deer take about four steps and just sort of fall over.....a great 200 yard rifle. You almost certainly have a three digit date code on it somewhere and close ups of the flats will likely tell the tale.
By the way, both .323 and .318 commercial rimmed ammo is available.
