I actually have a Lee push through sizer in .356 but it sits unused somewhere in one of my drawers. It's not the system that was at fault, but the .356" size is too small.
I know all the websites and reloading manuals say to size your 9mm boolits to .356" so that they're 1/1000 oversize from the standard .355". But following this convention, I got serious leading after shooting just a few hundred rounds in my barrels that even slugged as small as .355".
Don't laugh, but back when I first started casting I thought that if I sized bigger, like 2 or 3 thousands oversize, that my gun might kaboom due to increased pressure by plugging the barrel with a huge lead boolit!
Just because you shoot lead doesn't mean you have to clean lead from your barrel. If you do, there's something wrong. Some people freak right out at the fact that I rarely clean my barrels unless I'm putting them away for some time. But I figure if you're shooting and the bullet is obturating like is should, each shoot cleans the barrel of the residue left behind from the shot before
I shoot literally thousands upon thousands of rounds without doing a "proper" barrel cleaning. When you can do that, and there's no keyholing and accuracy is better than you, than you're doing ok.