I've never personally fermented uncooked soy, but it seems to be possible. Part of the reason why we use koji mold is to break down some of the more difficult sugars into other sugars that lactobacillis and other bacteria will eat. It would probably be best to break up the beans or mash them before putting them into the ferment so that it's easier for the bacteria to penetrate into the bean, or else it may take a very long time to ferment. A bit of live miso would contain a bit of koji and the right balance of lactic acid bacteria that works with soy, so personally I would add some to the mixture, perhaps even mixing in the miso and squished edamame first, then combining with your other ingredients.
Sounds exciting! Whatever you end up doing, will you let us know how it turned out, please? :)