Hi Kyran,
You have come to the right place. Congratulations on finding this gun. It is a typical smoothbore matchlock (Tanegashima-style) long gun from the Choshu Han in southwest Honshu, Yamaguchi Prefecture today. There are several striking stylistic features which tell us this at once, particularly those you have highlighted in your photography.
The signature is Kagoya (gunsmith House of Kagoya) Daisanzaemon/ Daisozaemon/Daizaemon/Daisanemon(?) (Just double-checking the possible reading of these personal name characters).
Kagoya Dai Sanzaemon...(best?)
籠谷台三左衛門 a smith from Sakai (Osaka today), where most of the Choshu Han guns were made to order.
Although not dated, we can assume mid- to late-Edo, before the advent of percussion locks when most of these original Choshu locks were adapted and updated. In fact in my experience it is not so easy to find an original example. There are however a couple of temporary fixes that someone has thought necessary to perform on your gun. By the way, did you take the breech plug out, or was it missing anyway?
That is the main body of information, while I try and double check how the smith would have said his name.