If you use the proper tool, the alignment is pretty simple. It's sort of like a cup press, there's a part that fits into the bottom of the head tube and a rod that passes through the tube around which goes the facer. Then you tighten it up and spin the facer a little to take it down. You only need to take off a mm or two. That would be the route I would go, but then I'm not a welder or brazer, so those things seem much more difficult to me.

Crap, facing a head tube is simple enough that Park recommends it prior to installing a new headset.