[Nazis] worked with the old officer caste despite its frequent disloyalty

I don't think the historical record supports this assertion. The Prussian / Imperial military was a parallel institution to the post-1848 civilian government - both loyal to the Kaiser, but otherwise unrelated. (No, this isn't a stable setup).

A substantial amount of the German army's political maneuvering in Weimar period was an attempt to maintain independence from civilian government oversight even after there wasn't really any German state separate from the civilian leadership.

Once Hitler took power, he broke the Army's independence (eg the destruction of Generals Blomberg and Fritsch). In short, the Nazis were the first civilian government to place the German military in a subordinate position. "Working with the old officer class" is terribly misleading.