You found the right vehicle. The things are even a bit more complicated. It was initially built by the Motor-Muli Schuster, Hacker & Co KG. Later on Saurer and Steyr were involved in the production, so I have seen it as a Saurer, a Steyr or even a Saurer-Steyr Motor-Muli.
One mistake in your answer has to be corrected. It was never used by the Bundeswehr (German army), but by the Bundesheer (Austrian army).
One more point for you.