When I subtract your playing surface dimensions from the exterior dimensions from the flyer in the photo gallery, it appears that each rail width, from nose to exterior edge is approximately 5″ which makes sense.
Your inside rail measurements confuse me.
I asked Dr. Dave from Colorado State why a table would be slightly longer than twice the width. He did not have an answer, and referred me to published standards.
It would be interesting to find someone who worked for Irving Kaye who might have been involved in the design of their tables.
I still think the answer is linked to the 1/3 table diamond system and the small playing surface. The size of the balls, pockets, and distance from nose to sites do not change, but the distance between noses does. So, as you shrink the playing surface size proportionally, the angles formed by the sites do not remain constant- they get more and more obtuse. Perhaps the elongation of each half of the table by 13/16″ was added to compensate for the angles growing less acute.