The 1903s from Springfield Armory with serial numbers below 800,000 are suspect. Many 03s were rebuilt at the outset of WWll with new bbls. Some are two-groove but don’t let this put you off, the two-groove bbls were surprisingly accurate.
It is said that in WWII the Germans came to battle with a hunting rifle (M98 Mauser), the Americans came with a target rifle (M1903), and the British came with a battle rifle (Lee-Enfield). The Enfield M1917 is the .30-06 version of the British rifle and also an excellent rifle.
I have gotten 3/4” groups with my 1941 2 grove barrel even thought the chamber is too big.