A lot of beasts have been done in with lead bullets .
Just use a 44 cal. bullet with a flat nose (round-flat or semi-wadcutter) for added "lethality" . Jacketed bullets will offer no advantage , the 44 Russian just can't be loaded to the velocity needed and for large critters (bears) you want/need penetration
to get the bullet into the vitals . Use a 240 grain Cast Lead bullet and a full charge of black powder or work up a smokeless powder load .
The Lyman Cast Bullet Handbook 4th Edition has lots of loading data in it, 5 different bullets from 185 grs. to 245 grs with ten different smokeless powders.
Personally ... knowing what I know , I would assemble a heavy black powder load for the old Top Break ...just like it was designed for ... don't think black powder is weak... a heavy charge is hard to safely match with smokeless and will hit hard .
Good Luck ,
Gary

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