My suggestion would be the 7X65R Brenneke, or should you like a little greater performance, the 7X75R SE vom Hofe.

Using a No. 1, you would not be limited to the loads recommended for break action guns, such as double rifles and drillings, so you could use the hotter loads recommended for the 7X64 in the 7X65R, and safely exceeed the lower pressure loads recommended for the 7X75R. A 26" barrel to maximize the effect of a rather low expansion ratio would not be a handicap in a single shot.

In both cases, the range limitations of your 7X57 would be extended appreciably, and you would not have to deal with the increased recoil of a .30 caliber or larger Magnum cartridge. Even though the Ruger rimless extractor works reliably, I always prefer a rimmed cartridge in a single shot, if one is available.