I have a question. You are in pursuit of an elusive pneumatic rifle, all stocks of which SEEM to have been concentrated within the borders of the Tyrol and all stocks of which were destroyed in 1809?
What arms manufacturer - of any age - is going to sell his wares ONLY within a small, mountainous province, with a relatively small customer base?
He / they must have hawked them around other places, in particular the Austrian military, certainly the biggest domestic market.
Troop trials would surely have been carried out and records of these trials would exist.
I imagine these guns would have been relatively expensive, due to the high machining standards required, further limiting the market.
Girandoni`s guns fell out of favour with the Austrian army because of the high cost of maintenance and repair. How could a Tyrolean peasant-hunter afford this extra burden?