Japanese 19 Piece Checkerboard Puzzle

Made in Japan circa 1940.
(wood box 3.8 by 3.75 by 7/16 inches thick and 19 wood pieces;
wood inlays on the box cover are 5/8 inch diameter;
paper stamp on the back is 1/2 inch square)

Purchased from someone who remembered it from his childhood in the 1940's. At some point in the past the following solution was drawn:

This puzzle has the same dimensions, style, and cover inlays as the 16 piece puzzle on page 233 of the Haubrich book. However, even if one assumes that the 1x1 pieces broke off of larger ones before the solution above was drawn, and taking into account rotations and reflections (the pieces are double sided), there is no way to make it the same (and no way to further combine pieces to make it the same as the 14 piece puzzle of the same style on page 177) Here are the 16 pieces if the 1x1's are joined to the pieces above them in the solution above: