Thanks. By the time I got around to this post, I was thinking more about performance rather than it's interesting history.
Airguns known to have been constructed in Tyrol are extremely few and far between. They just don't exist in Tyrollean museums, for reasons I've explained before. Cortina d'Ampezzo was burned to the ground during the Napoleonic wars in retaliation for continued resistance. Then, anything that escaped that were burned on orders from the American army at the end of WWII. Two of the only three known Tyrollean air guns are located in museums outside of Tyrol. The other one is located in Cortina d'Ampezzo and appears to have been built by the apprentice of Girandoni (that unique airgun that demonstrates how to achieve variable power in these airguns)
I did remember to forward this picture and info to the museum director in Innsbruck.