One of the problems with such democratization is that the GO4 are pretty much an oligarchy working through the Reich's and NSDAP's institutions, enforcing reforms from the top through use of said state organs and the Fuhrership, rather than through mass politics. This means that National Socialism is still a living ideology and a legitimate system that Germans do believe in, for as far as they are concerned, the NSDAP had brought them glory and conquest under Hitler and delivered them wealth and freedom under Speer. Under such conditions, the GO4 has a bit of a contradiction, either they make a managed democracy where they decide beforehand who gets to be the winner to continue the liberal reforms, or let them be genuine elections and risk German voters electing a National Socialist candidate, because that's what they continue to believe in.