That is the same version 760 I used to own in .30-06. The only .257 Roberts I have ever seen in a Remington 760 is still possessed by the 70 year old man who bought it new, and the rifle is just like yours, the old style.
A nickel can be cut and gound to fit that slot pretty nicely. Used to be, Brownell's offered blued steel inserts for closing the slot.
BTW, that old 06 760 was very accurate and quite solidly built.