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Thanks for sharing that drawing.  It does look like that screw would fit.  Now, the challenge of finding one.  I will look for that book as well.
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Since this first model was immediately following the Trapdoors which used a convex screw, you might try to find a later trapdoor from which you can "borrow" a screw to test the fit.  I imagine, that SA would try to use up old inventory wherever they could.  When I think about it, I think every butt plate that Springfield used from, at least the Model 1842 which is as far back as I can look at, had convex screws.  There should be some available at many shows.