Sounds like you figured out the slug part. FYI - some fussy people will get slug inch or two into muzzle, than inch or two into throat - to compare - if your slug was pushed all the way through the barrel, is going to give you the smallest diameter that it was subject to. Your throat area, chamber area or muzzle might be larger than that - up to you if that is important information or not. Is some amount of things to play with, for cast bullets - is not just the sizing / fit to bore - also lube, loading (velocity), etc. to get results. But in the end is what you are after - where do holes show up on target - might be good enough on the first go at it.
Rough rule of thumb, for many, would usually be that if barrel slugged to .379", then you would want a .380" or .381" cast lead bullet. Various ways to get that - including powder coating, I think.
Was also, about forever, thought to scrub out all possible copper jacket fouling from a barrel before trying lead cast bullets - other posts on CGN, recently, have suggested that has been shown to not be such an issue - but I still think is one of those things to consider, if you are trying to figure out why you are getting 6 inch 5 shot groups at 25 yards - some "thing" is not as it should be - sometimes is hard to always pin down what that "thing" is.