The parameters of this question handcuff the designer somewhat, much the same as it did back in 1910. The reason we had the designs that we did in 1910 is because nobody then wanted to take any chances in designs that might be considered a "non standard technical leap". Sir Charles Ross gave it a try, and look what he got for his trouble...
Since the P14-M1917 was technologically possible, although not designed until around 1913, I'm going to go with that, but with a 24" barrel instead of the 26" they actually used. It's an extremely sturdy rifle with an action that had plenty of mechanical "camming" which would be great for the oversize British ammo that was soon to follow.
If we were to go with designing our own cartridge as well, then my answer would be somewhat different.