I'm with Peter. There are a number of local German and Scandinavian fellows who use Drillings and overunders (rifle on top- generally Keighoff) for hunting and they all use Brenneke's for the shot barrels. In testing, these usually shoot close to the sights.
I am not a fan of shot for large game. My cousins in Ontario have had poor 'luck' when shooting whitetails with buck shot in their shotgun-only hunting areas :- too many lost, wounded deer. After switching to slugs, they stopped losing deer.

Make the rifle barrel work & do not rely on a 'fast' second 'shot' of anything, but do test with Brenneke's first.