I have read a bit of David Cushman's writings, but not the bit about "Cold Way or Warm Way". It also hadn't registered in my brain that British Standard Hives are square. Thanks for the link Moots.
Like Mr Bush said, I had considered the similarity with Dadant (and Warre) style hives, but the initial bit of Dadant history I found only mentioned 10 and 11 frame Dadant hives. Michael do your bees use all the frames in your 12 frame boxes or are they reluctant to get to the outside frames like many hives are with 10 frames boxes? I suspect that the number of frames may have more of a bearing on the frame spacing/comb width than anything else (most of the time).
Maybe offsetting the layers of boxes helps with access for the bees - potentially, any frame is accessable from any frame in the layer below (or above for that matter). There might be some advantages with heating and ventilation as well??? As with most things in life, beekeeping is a sea of compromises, fix one thing for summer and make yourself a problem in winter, get nice square boxes that the bees like but very few use, so you can't buy off the shelf supplies.... interesting design though.