mbatten,
You might try conical bullets intended for 36cal cap and ball pistols. The max diameter is .375, but it's such a short section at that diameter that it shouldn't make a difference as long as it chambers. The base section that stands in for the "heel" is very short so it has to be handled carefully. Lube with Alox or spray lube. My cousin uses them in his .380 Rook Rifle.
Mike