Hi Don,
I actually saw that USAF Museum Dora last week and also noted the wood prop (which was standard on the type).
Indeed the strategic materials explanation has a lot to do with it. But the Luftwaffe has used wooden props on earlier types as well (the Ju 88 and He 111) come to mind, so I am not sure if that's the full explanation. Perhaps they're also cheaper and quicker to produce?
I doubt service life would have been a big issue. Most aircraft probably didn't outlive their props in combat...
