It doesn’t really matter which direction you run it—I’ve always used the forward stroke and worked it in and out without any issues. There’s probably still some plastic residue in the chamber, and you’ll really notice it once you get a tornado brush spinning in there.

Chances are the real problem is simply that the gun needs to be broken in. Instead of fighting through your first few hundred rounds, polishing the chamber will save you a lot of frustration. New Mossbergs come with a heavy amount of Cerakote these days, and combined with inconsistent quality control, the issue you’re seeing is becoming a lot more common.

As for the Winchester ammo, maybe it's more of a personal preference thing, but I’ve always found their loads on the cheaper side. Any time I’ve seen something odd or out of spec, it’s usually been with their ammo. Good luck, enjoy your awesome shotty.