Here is JB's data from "Loads that work"
.257 Roberts:Like the 6mm Remington (the same case necked down), the .257 Roberts does fine with one powder. The traditional choice is IMR-4350, but Hodgdon’sH-4350 works equally well – and better in cold weather. Around 46grains works excellently with 100-grain bullets with velocity about3,000 fps, plenty for most deer hunting. For larger deer I’ve mostly used the 115-grain Nosler Partitionand 43.0 grains of H-4350. Velocities run right on the heels of the100-grain load noted above, and the bullet is more reliable on really big deer
I would follow Barnes recommendation on seating depth or Bergers. Most monos like some jump. I load them up to within a grain or grain and a half of loads for max loads for conventional lead bullets. I would try annealing the cases especially the Winchesters. The +p cases may have lower capacity so check this. I haven't found the Roberts to be finicky at all to load for. If you want really good cases neck down some RWS 7x57 mm brass, check for thick necks.
