Your table not being twice as long as it is wide is strange from a systems point of view. I wonder if that contributed to the adoption of the 3 x 6 grid? As the playing surface shrinks, but the distance from the nose to site does not change, altering the angle between sites, if employing a diamond system.
I would be interested to get your feedback on comparing what banking relationships you find on your table compared with the relationships I found on my 8′ table which is exactly twice as long as wide.
Although the stories you have heard about the tables being narrower than normal proportions to fit more in a pool hall is plausible, only saving an inch hardly seems worth the effort if your table plays funny. It seems unlikely as there is not a standard size of a pool hall, and the additional width to make the table I’ll bet the decision to make the table slightly elongated was not a casual decision. Kaye had to have known that if his table played differently than others in the industry, he was at risk of losing customers. I suspect the decision to employ 3 x 6 sites was related to the length being 2 x width + 1 5/8 inches. Unless some architectural archives are discovered, the reason for the non-standard length/width relationship and the non-standard site placements may be lost forever. If you find there are a lot of additional banking options than you would find on a standard table, I think that would solve the mystery.