Personally that looks like a typical Funnel type lead that was common back then. I don't think I would do a thing with it till you shoot it using proper bullets in it. Every BPCR rifle I have has that type of throat except one and they shoot quite well.
The photo below has a throat similar except it's not a bottle necked case but the lead is close and it will hold it's own for accuracy.
With all due respect, the 8 X 56 RD is, and was designed as a smokeless cartridge, and the pressure curve there is going to be hard put to provide the "bullet bump / slug up" that sorta' throating calls out.
At this point BP is WELL worth trying, and it would be no big deal to equip that rifle with a wiping rod, for field cleaning.