I personally cannot envision a whippier barrel than one that's swamped. I envision that enlarge end making circles about a central axis.
If I had a swamped barrel, it would be propelry bedded in glass, full length - or, at the breech and muzzle only, floated in between - the other alternative for full stocked firearms, antique or modern.
Of course, unless fulled bed in wood or glass, the stock would be even more fragile.