Hike and Bike.
This is a very long hike. We did it with normal bikes which is adventurous and challenging but doable. We ended up dropping the accent to Birkkarspitze, but without the beak at the hut it is differently possible to also do the peak and still catch the train.
From Scharnitz It took us 2 hours to bike to Angeralm. We left the bikes there. The loop to the hut took us 6.h 30min (not incliding the accent to Birkkarspitze) so we were at the hut 17:30, where we had a break and some food.
We were down at Angeralm at 19.00 and at Scharnitz trainstation at 20:15. So we had some time to kill before the train but as the last train back to Munich leaves 21.30.
Read more about the hike at www.hikingwonders.com