Seems doubtful the free-bore is the problem.
All Weatherby calibers in all Weatherby rifles have what is considered excessive free-bore in other rifles & calibers.
They do it to control pressure, not only during normal shooting, but in extreme temperatures, in Africa for instance.
I think I would investigate jacket fouling in the bore, a damaged crown, loose scope mounts, a marginally bad scope, loads or bullets the rifle doesn't like, or a stock bedding problem before I got too concerned about the Weatherby free-bore causing accuracy problems.
And no doubt about it.
A .375 Weatherby isn't the easiest gun in the world to shoot tiny groups off a bench with!!
I don't care who ya are.
rc