HOLD_UP there folks!!
Remember, both Remington & Winchester were contractors for supplying the P14 British .303 rifle prior to switch to the U.S. Rifle, Model of 1917.
I have seen Winchester that was in .3006 that was accepted by the WAR Dept, before all inspection procedure were finialized..
SO, we need some photo's of the top reciver ring surface to see what markings are visible.
Have your noticed a "broad arrow' marking anywhere on the rifle surface.
If so, THEN might be a .303..
Best way is to have a smith do a chamber cast and measure against known chamber drawing, THEN you wil know for sure.