I've used jacketed bullets over black powder with some success, however, the bullets were Hawk and they are annealed dead soft for copper, about 25 BHN I believe, which is just a little harder than linotype. Best results have been with a lightly duplexed load altho straight black was satisfactory.
My belief is that the jacketed bullets from the big bullet manufacturers is entirely too hard. Hawk manufactures bullets with two different jacket thicknesses and as stated above, annealed dead soft, and are the only bullets I've used or would recommend with black powder.
Reason for their use was a badly pitted bore in an original rifle from which cast bullets wouldn't stay in a 5 gal bucket at 50 yards.
It's interesting that your rifle, such a small bore, is more accurate with jacketed bullets. Just more proof that each rifle is an entity unto itself an a person ought to try something before condemning it.
Vic