Have you tried the rifle at the range? And tried it on the bench? My question is not facetious. Back in the day when 03A3 rifles were being sold off, somewhere in the $40 range, serious shooters looked as closely as possible at the barrels. No bore scopes back then, but it doesn't take much to slug the barrel. Sometimes the 4-groove barrels had pairs of grooves with different dimensions. I have one with one pair of grooves measuring .3080" and the other pair .3085". Later production barrels had only 2 grooves and some were reported to be more accurate than some of Remington's 4-groove barrels. 50 % less opportunity for error?

The 03A3 action is stronger than all but the last original 1903s. The original bolt was either worked over or replaced. The stamped bottom metal was replaced. The stamped magazine follower was retained. Some of them worked more smoothly than milled replacements. Whether anyone likes the treatment or not, this was not a cheap sporter conversion. Good quality replacement barrels were available for somewhere around $100. Why retain the Remington barrel?