Weaver recommends these bases for the 1903 Springfield:
http://www.weaveroptics.com/mountcharts/default.aspxRear 54
Front 55
Use the dimensions of the 54 and 55 bases to see if an 0.860 spacing base is close enough to use, maybe with a different height rear.
http://www.brownells.com/.aspx/lid=11214/learn/W_R__Weaver_Company_Mount_Base_Specifications75 looks like it would work on your front, instead of a 55.
Once you get Weaver bases on it, you can use many different maker's extension rings to fit a short tube scope.
Bruce