The funny thing about that rifle was it was shooting about 10" high at 100 yards!!! I had to hold way low on the target, just to keep them in the black.. Later I bought a new front sight to bring the elevation/POI down where I needed it.
What you were experiencing is that those sights are set up for a "battle zero" . 1903 Springfields are set for 547 yards (500 meters) and yours were set for a similar distance. Those were pre dial twisting days.