I don't chamfer, except after trimming. I do not trim semi-auto pistol brass. I just setup my case bell to bell just enough to allow the base of the bullet in. I then take the bell out with my bullet seating die and crimp with a Lee FCD. I think the chamfering idea sounds like a huge waste of time.
I get what you are saying about cleaning. Since I do not have issues with getting my primers seated properly deep, I will continue cleaning first and the sizing. The media in the flash hole is a very real issue. On rifle, I decap first and media is in the flash hole so much that I put the decapping die in the first station before I load the ammo.