That is a lovely rifle and chambered in my favorite round, EFR. I would try the 160 Partition or a 175 and maybe a 150 mono to see which is more accurate. The 7x57 has proven itself and, no doubt will continue to do so.
It might have had more to do with the Remington Rolling Block military rifles that were chambered in 7×57 for South American customers. I have read a comment, possibly in Rifle or Handloader magazine, to the effect that some of those rifles had grossly excessive headspace. I am currently in the early stages of reshelving my book/magazine collection and need to do more work on my list of references in order to better access such entries, on demand.Longwalker makes a good point there on ammunition. American factory ammo is rather pathetic. This is/was to avoid the older Mausers, 95,96, caving in under more robust loads.
European ammunition is loaded more to the full potential of the 7x57.
Have a look at Rusan Rings, I get mine from optic trade. nice rings reasonable price. It will just take a bit to get them in the mail.I'm currently shopping for scope rings