If I remember correctly, (and my memory is suspect at my age) I read somewhere that the 1903 barrels took .267" bullets, which is why I planned to try them.

I tried the .264" bullets first, then determined that the .267" bullets would pass easily into the mouth of the fired case, and went with the .267" bullets. I also have a military 1903 which was rebarreled with a .264" barrel, and it, of course, shoots .264" bullets accurately. A cartridge loaded with a .267" bullet will not chamber in that particular rifle, so there's no risk of firing the wrong ammunition it. I have two original 1903's, plus the one Carpetsahib now has, and all shot best with the larger bullets.

Incidentally, I found that Sellier & Bellot factory rounds work well in my rifles, although according to the information published on their web site, they no longer offer ammunition in that caliber.