Could just be the mighty power of Makita but if I put a cup brush on my angle grinder, one touch = shiny metal. Particularly on that head where there isn't much to remove. Plus a cloud of stuff that you don't want to breathe. Insert dust mask advice here, but no, it needs to be a respirator. Just me, but vinegar all the way, or leave it as is. No wire anything. Vinegar for an hour or two, hit it with a scotch brite or scrubby of some sort just to knock off the stuff that the vinegar loosens. Keep going until it's at the level of clean you want. I'd grind the mushrooming. You can use a hammer to pein the ground area to blend it - do it before vinegar. Vinegar will help blend it further.
Grinding out the pits is only if you want a shiny new looking axe (and you have lots of time you just can't stand to have anymore) and you risk damaging the mark, which looks a little shallow in a couple spots anyway. Pits are a non issue IMO.
