First - disassemble and really clean the piece.
Look for burring as you do, and stone that away - being careful to not change any factory angles.
Reassemble with a 'good' lubricant - and try.
you may find that you've solved your problem.
As to the muzzle - you can re-crown the barrel fairly easily - and that will greatly assist in accuracy.
Use a half-round stove bolt and sandpaper of different grits and go slow.
Since you're not touching the exterior of the barrel - your finish will be fine.
Rust is one thing - pitting quite another - you can clean a lot of it with over-sized bore brushes.
Vaya,
Scouts Out!