Funk is a well respected name, in any case case members of this family work in suhl till WW 2. have had a combination gun in my hands, breechloader, with 20 ga shotgun and 24 gauge rifle barrel, making arround 1900. was a fine gun like yours.
I would load this gun with 70 -100 grain Fg and a 500 grain Minie . the gun wasnt made for Miniebullets but its maybe the best way, please check the barrels. I will look into the british militaria forum for a case with a german jaegerrifle, wait a moment.