Thanks for your answer, Steve: BGH history seems really exciting because it is probably so representative of the history of hat making in the late 19th and early 20th century - not only (Daniele told us similar things e.g. from Monza), but also in Germany. There is still much to discover...Matt, Thank you! Other than the two "Aquila" Stiff Felts there is only one other original BGH brand hat that I am aware of and it's also a Stiff Felt that belongs to Stadt- und Industriemuseum Guben.
I made a list of the WWII era and older no company brand Wool hats that might have been produced by BGH. I will update the list and send it to you again. From what I can remember you made a connection with the 3 gate / tower Guben coat of arms with one of the hats. There are also the similar paper labels. This "Dogma" brand Wool Soft Felt is a recent example. Did you see this hat?