Parashooter,
You got me again, looked it up on wiki and I should have said M1903. Some of the early design and testing was done in 1900 of models that led up to the M1903. Not sure if I ever held any of the 03 Springfield in my hand. Got 2 1917 Enfields and 2 Krags and am forgetting stuff faster than I can learn it.

BR,
You may be right on the sight before the threads. On the far right of the spindle tube (on the threading machine) there appears to be some hardware that may be for aligning the sight base. If this guess is correct there would have been a different spindle or tube for rifles and carbines maybe different but similar machines. 
If you looked at enough sight bases you might be able to figure out which side the screw tightened to align the sight for threading and maybe the rear sight drilling and extractor cut. Assuming all work was indexed from the sight base, it would have been from one side or the other not a theoretical center of the base.
From the tone of the article Pratt & Whitney did not build all the equipment. More details would have answered a lot of the questions we have asked.