Hey Peter,
I did a little resolution building with a make-shift notation for the microtonality. I wanted to see if there exists something like a '36-tet dominant chord', something that sounds even more dominant than the normal 12-tet. I didn't find anything at all, but I still think both resolutions sound kinda cool. For the first one I tried resolving with smaller intervals, for the second I used bigger ones. I think you're right about the supermajor chords - I'm not really a fan either.
About that E-1/6-flat that was made to sound like a perfect third (just intonated third): I didn't perceive it as such, and I think I know why. A perfect third is a little less than 14 cents lower than 12-tet (according to https://en.wikipedia.org/wiki/Ptolemy's_intense_diatonic_scale), and the third of the dominant only 12. So by lowering that E by 33 cents, you overcompensated, and ended up further away from the perfect third (5 or 9 cents further, but flat instead of sharp).
Kind regards,
Marius