Maybe the twist is the determining factor here
After reading Jim Love's take, I can see his point. Maybe the slower the twist the better the fit. If I did a 1 in 13 inch twist, then the shorter bullets for the improved .257 Rob'ts wouldn't stick out too far. But going to solid copper, might be counter intuitive. But an improved rifle cartridge should, IMO, be able to accurately shoot at least one weight of bullet, loaded in present factory ammo. A one in thirteen or fourteen twist may indeed use a short enough bullet to fit in a 722, but what factory round would it also shoot? Remington flipped flopped on it's 244 Rem.. First it was too slow, then later, it was a little quicker than needed. If I put a 1 in 14 twist barrel in a 257 imp., then it would be truly exotic, but it would be more of a 250-3000, extra long.
So a 25-284 with a short throat, and a 1 in 10 twist, would cover the wildcat end, and a 257 imp. Roberts, would cover the improved end. But to get to the hot rod trajectories of the lighter bullets in the old 244 Remmie, you need some more room for the powder, in the quarter inch bore. And whatever you come up with, It's gotta feed smoothly through the 722. These same parameters doomed the original 6mmRem BR. It was left to Norma to figure out what to do with that case. But neither of them feed worth a hoot. So I'm guessing that using a 722 means that he wants a repeater?? But I would have thought that Remington would have learned their lesson, with their 244 Rem debacle. But I've reluctantly given up on ever buying a box of factory ammo with the 100 gr. Remington Core-Lokts, for my Rem 6mmBR rifle. They are just too hard to find. Whichever version of the 257 Roberts, he uses, it had better shoot accurately with the 117 gr. factory ammo. Then at least he has a loaner rifle, that will be safe for an in law or friend to hunt with. What we are building today, could well, come out of a grandchild's closet in fifty years. And all things being equal, the factory ammunition will have the much longer shelf life. Fifty years ago, who would have thought that wild hogs, in the South, and Canadian sub arctic timber wolves would be so menacing today?