Guys, this is a Springfield M1903A1. It's pretty much the same rifle as the M1903 used on "Top Shot", save for the C-type pistol grip stock, which Uncle Sam in 1928 considered superior to the straight grip stock of the M1903. Many M1903 rifles were actually converted to M1903A1 configuration as they were rebuilt at government arsenals between the wars.
The stock ain't the problem, though. The rear sight, however, is. Lemmee 'splain, okay? M1903, M1903Mk1, M1903A1, and M1903 (Modified) rifles all had the windage-adjustable rear ladder sights that were zeroed for 547 yards, aka 500 meters, when the ladder was down to expose the V-notch. Back in the day, almost all the infantry-length (and even shorter variant) rifles of standing armies had super-long battle zeroes, be they Springfields, Swedish Mausers, Schmidt-Rubins, 98 Mausers, Lee-Enfields, you name it. I won't get into the semantics, but it was part and parcel of military tactical thinking back then to engage at distances somewhere between 300 meters and "volley" range. Some rifles even had separate volley sights mounted on the side, my NoIMkIII SMLE being one prime example.
Now, this is just an observation from watching "Top Shot" the other day - you were probably fighting that 547 yard battle zero. If you were using surplus M2 Ball ammo like I think you were, that means your point of impact would be 7.3 inches HIGH at 50 yards. In other words, you'd have to hold under 7.3 inches to centerpunch the 50 yard bullseye. Going out to 100 yards, it gets even more fun, with nearly 14 inches of hold under required to centerpunch the target at that range.
Doughboys knew that. My fellow Camp Perry shooters knew that. Many of us "cheated" and used the 1903's bottom peep aperture found in the ladder when flipped up to the vertical. The bottom peep is zeroed for 100 yards, which makes things a heck of a lot easier than using the 547 yard V-notch. Just sayin'...
Of course, were it up to me, I'd have used the 2.25x power scope as issued on my M1903A4 Remington sniper, itself based on the peep-sighted M1903A3 Remington (Springfield) rifle, but that's just me.