1903A4's were pretty standard in scope mounting...
Redfield Jr. mount, you're looking for the ones with the square edges, more recent versions are beveled at the corners. The rings are the ones that are split at the top, if you're going for an earlier, WWII 1903A4. Those rifles used the 3/4" Weaver 330C scope, with the 7/8" Lyman Alaskan as substitute standard. Both scopes had a military designation, the Weaver 330C was called the M73B1, while the Alaskan was called the M73, authorized to replace the Weaver late in 1944.
By adding a rain/sun shield and rubber eyepiece to the Alaskan, the M81 and M82 were born. These scopes are seen more often on Korean War and Vietnam-vintage 1903A4's. The M84, with it's metal covered turrets, carried the refinement of the Lyman Alaskan family one step further. This scope wasn't available in quantity until well after WWII, and was most commonly seen on M1D Garands, although it was also issued for use with the 1903A4.
There are also Redfield Jr. 1" diameter rings that worked with the Weaver K4-60 series of scopes, sometimes seen on Vietnam-era 1903A4 rifles.
BTW, are any of those Springfields that are drilled and tapped bearing offset serial numbers on the receiver ring?
The info I have states that scant stocks were used as replacements at depot-level refurbishment locations. The 1903A1, of course, had a full C-Stock (basically the only thing that differentiated it from the 1903), and the 1903A3 usually had a straight grip stock. The 1903A4 could be found with either the scant stock or the C-Stock. My Z-series 1903A4 deer rifle restoration above wears a DuPage Trading Company reproduction C-Stock. I don't know if they even offer them anymore, but Boyd's does. Here's an October 1918 1903 I found in a pawn shop that had been arsenal rebuilt to 1903A1 configuration:
Steve, what *hotter* ammo are you talking about? Hotter handloads, M2 Ball, or Hornady Light Magnum? M2 Ball was standard issue fodder for both the 1903A3 and M1 Garand, no reason not to use it, or a ballistic duplicate, in a 1903A3 that passes a safety check by a qualified gunsmith...