James, members of the Hills family signed their names on the top extension of the butt plate. I've seen several guns signed by the gunsmith Medad Hills in that manner.
You are most correct Fullstock.
My mind naturally goes to English made pieces while the OP's post clearly says is concerning British "style" fowling pieces. I should have caught that but I see "English" and run with with it sometimes.
I assume British "style" is referencing the term Mr. Grinslade uses to describe the New York and Phili. guns that resemble the large English waterfowling pieces.
I believe most of the names found on locks of these styles of guns were of the lock manufacturer like Wilson, etc.
If I recall, the barrels in Grinslade's book are for the most part unsigned except for proof and maker stamps. I believe some of the PA British styled guns are marked Philadelphia.
I am working on a English piece that is in cherry and will have the same problem as you Dave K.
I am looking at two routes. ...
1. a restock of an English gun as if all components of the original English made piece were used. The the barrel or lock (or both) could be signed with the "original" maker's name. In this case it would be my name.
2. An English "styled" gun as if using an import barrel and lock. In this case I would use my English styled maker's mark at the barrel breech of the barrel along with the proofs and just engrave my name and date on the bottom of the barrel.
I am probably going to choose option 1 because
a. The barrel is only 40" and is more suited to a birding/sporting piece than a huge duck gun.
b. My interest is more in the south where imported complete guns were predominant.