I too have fallen under the Ruger #1's spell. From the minute I saw the first ad in 1967, I just knew I had to have one. Over the years I have bought, sold and traded for over 19 of them. I managed to limit my addiction and have kept only 7 of them.
Some of them had crap (technical term)...
The 257 Roberts is a sweet little cartridge as is the 260 Rem or 6.5x55. However, when I built my mountain rifle based on a Remington model 7. I had it chambered by Pacnor for a 270 IHMSA which is a 300 Savage necked down to 270 and never looked back.
I would remove all of the bedding and rebed the whole thing. You are assuming that the receivers are EXACTLY the same. I have a couple of Remington 700's that would prove you wrong.