Just two points, Brithunter - er, Turkeyfeather
That rifle should have the 1902 Remington #1 Smokeless action, and so should have been made with the proper, smaller diameter firing pin tip - and shouldn't need bushing unless the breech face is corroded, etc.
Those older guns have softer steels, and will wear appreciably with repeated jacketed bullet shooting. It might behoove you to shoot cast bullets, or rebarrel with a new steel barrel if you want to do jacketed.
BTW - DeHass mentioned that the easiest way to make an excess-headspace 7x57 RB rifle safe/shootable is to simply recess the breech face of the barrel so it will chamber the 7x57R cartridge - since those rifles were also made in that caliber.