Your idea is very new and interesting, the graphs are visually appealing (well, the researcher shades do look like puke,
Aiss, in all seriousness it doesn't matter) and easy to read. The problem I run into when thinking about these new divisions is that, clubs are attributed to certain quadras and not others for a reason, that is, the nature of the club speaks about the nature of the quadra as a whole.
Beta and Delta NFs are alike in that both ego functions are internal [(Ni + Fe) and (Ne + Fi)]
Beta and Delta STs are alike in that both ego functions are external [(Se + Ti) and (Si + Te)]
Alpha and Gamma SFs are alike in that the ego functions are split internal/external [(Si + Fe) and (Se +Fi)]
Alpha and Gamma NTs are alike in that the ego functions are split internal/external [(Ne + Ti) and (Ni + Te)]
Beta and Delta NFs are alike in that the ego functions are split involved/abstract
Beta and Delta STs are alike in that the ego functions are split involved/abstract
Alpha and Gamma SFs are alike in that both ego functions are involved
Alpha and Gamma NTs are alike in that both ego functions are abstract (making NTs the sexiest type)
I am sorry if this is all redundant to you, but it's my understanding of why clubs are useful and at what point their attributes and viewpoints become specific to quadra. I feel that your proposition, while interesting, is unnecessary.