Hi Jacek,
at first I skimed over your essay and found it interesting. Actually I used the exceptional geometries (NIL, SOLV, SL2) in my work. In a previous paper I described the interaction with them (see the paper). The idea is simple: the connection between the knot complements (=fermions) are torus bundles and there are only 3 types of torus bundles which can be identified with interactions (weak, strong and EM). In this paper you will also find the identification of bosons to the geometries.
Currently I think about the SL2 geometry and the Ricci flow.In the past I thought that the Ricci flow is something to do with the measurment process in quantum mechanics but now I changed my mind. I have to go over your essay more carefully. Thanks for your words.
Best Torsten