I've read Zitelmann's “Hitler’s National Socialism" and I think you're misrepresenting his arguments if you think he's arguing "Hitler was a socialist". It's much more complicated than that.
Again, this might work if your own arguments weren't written in half chewed crayons. But alas.
Hitler wasn't a socialist. He wasn't a free market libertarian either. He saw value in elements of both systems.
At the end of the day, every single school of socialism includes the necessity that the means of production are held by the workers, either directly through cooperative or collective ownership or indirectly through representative democracies. Given the Nazis did not own the means of production and were not a representative democracy, they were not socialists.