RE: Problems with Moss 935 Slug barrel
Assuming you have verified that the barrel is in fact rifled, I'd say it doesn't like those other brands. Can you see rifling?
I always suspect the mounts and the scope itself, but you say the 'hammers shot good. If you have time and the inclination to mess with it, tear it all down, degrease screws and holes, remount with lok-tite, and try again.
Otherwise, shoot the 'hammers.