Howdy,
My Dad has an old '86 Winchester in 38/56 that has a worn out bore and gives similar troubles. we finally found a fix, but its kinda extreme, You might be able to fix it by using a softer bullet casting media, the old Winnys had bores that varied in size and depended on the soft lead sealing the bore simular to a muzzloader, (according to Mr. Tappin) it works, but cleaning lead out of a bore can be less than fun.
We also tried sizing some hard cast bullets down until they fit SNUGLY inside a well annealed .380acp or 9mm case. The seating the bullet inside the 9mm case (um, remove the primer and make sure it is fully seated) and load like regular jacketed bullet. It takes some time and fiddling with and some equipment you may not have,They aren't much good for anything but punching paper, but they shoot a lot more accurately in that oversized Winchester bore.
And no lead fouling, but it takes some tinkering and special equipment.
JMHO
BT