Looked it up... .308 is roughly .473" time to sketch something out. You think it would be okay if the wood was the same diameter as the tamping head? Or should it be a smaller diameter?
I don't think it would be a problem. The old-timer tampers are just a piece of wooden dowel. Thing is, you're a blademaker, right? Why not put a handy little reamer, spoon thing on the other end.