I think Berchtesgaden National Park is a no-brainer here.
This site has valuable tips on how to spot the local "speciaties" there, unfortunately only in German (maybe Google Translate can provide a legible translation?).
The site lists the following species for Berchtesgaden NP:
Gänsegeier (Griffon Vulture; may possibly count as feral, see details),
Steinadler (Golden Eagle),
Wespenbussard (Honey Buzzard),
Wanderfalke (Peregrine),
Alpenschneehuhn (Ptarmigan),
Auerhuhn (Capercaille),
Birkhuhn (Black Grouse; apparently still lekking at this time of year),
Haselhuhn (Hazel Grouse),
Rauhfußkauz (Tengmalm's Owl),
Sperlingskauz (Pygmy Owl),
Schwarz-, Grün-, Grau-, Weißrücken- und Dreizehenspecht (Black, Green, Grey-headed, White-backed, and Three-toed Woodpeckers),
Felsenschwalbe (Crag Martin),
Bergpieper (Water Pipit),
Alpenbraunelle (Alpine Accentor),
Ringdrossel (Ring Ouzel),
Berglaubsänger (Bonelli's Warbler),
Zwergschnäpper (Red-breasted Flycatcher),
Wasseramsel (Dipper),
Mauerläufer (Wallcreeper; rare),
Tannenhäher (Nutcracker),
Kolkrabe (Raven),
Alpendohle (Alpine Chough),
Schneesperling (Snow Finch), and various others.