If we were being really sensible, the World of IHMN projected forward through the Great War (whenever that happened, if it happened) and into the '20s and '30s, would likely be so fundamentally different that none of the entities you named might actually exist in that future. There might be no Great Depression, Germany might become a Proto-Hippie state, Huey Long might have become president... you name it.
or
You could just do what IHMN did for Steampunk and create a whole new Dieselpunk World with no connection with IHMN, which actually gives you far more freedom without the need to try and get it all to marry up. Crimson Skies type break-up of the U.S., no problem... no Nazis but a surviving Imperial Germany, no problem... whatever you want.
I'd be far more interested in a Dieselpunk setting, but IHMN was very 'Victorian' (as it should be), the zeitgeist of the '30s would be more 'American', even the Nazis feared that Jazz threatened their very survival.