I will add, that it is worth reading the actual NSDAP platform: http://www.hitler.org/writings/programme/
You neglect the obvious fact that Lenin and Mao–ALL Communists in fact–ALSO outlawed labor unions. Does that make them conservative?
Conservatism has two principle strands: respect for the past–and for coherent moral narratives based upon them–and free markets. Hitler completely repudiated the moral ethos of the German nation, and under him markets absolutely were not free. They were much more like the relationship between Barack Obama, Wall Street, and Big Business generally, like GE, and Berkshire Hathaway.
Culturally, National Socialism (I did not see you note that the full name of the Nazi Party was “National Socialist German Worker’s Party; or that its principle constituency was the working and lower middle classes) did invoke the German past. In that it did not try to completely invalidate every aspect of German culture, it was less radical than Communism; but clearly what it brought was revolutionary, not a part of actual German history.
And again, economically, the only difference between Communism and National Socialism is that in the former all means of production are controlled in ACTUALITY by the State, and in the latter they are only controlled in PRINCIPLE. In both cases the right to the possession of the results of ones own efforts is non-existent.