The thing is, custom bowyers, particularly top of the line ones like Blacktail, tiller their bows individually so that the top and bottom limbs bend equally, when gripped either split or 3 under, whichever the bow is designed for. So while 3/8" does seem on the high end to me too, I have to assume that's where the limbs bend equally for that particular bow. I suppose you could test that yourself by putting the bow on a tillering stick. Another indirect method of testing it is to bareshaft tune and see where the nock point ends up, which you state that you have done. If you're getting level or slightly nock high arrow flight with a normally positioned nock point, that would be an indication that the bow is tillered correctly.
If the tiller seems correct for that particular bow, then you just have to go after the normal culprits, like string slap, silencers, noisy takedown connections, etc. Some bows are just noisier than others, I guess.