Shooting is not cleaning whatever the bullet you shoot.I think you'll just iron the lead in the grooves and we all know that once the process of leading has started it keeps increasing.
Clean properly and find what causes the leading would be,as suggested the proper way.
Think of it:we shoot no GC lead bullets in rifles at 1300fps without leading and so why would a handgun be different?If it can be done in a long pipe so can it be in a short one.