For the headsets in question, the Hozan lockring wrench should work just fine for the lockring, and is probably the best quality tool for the purpose. For the top nut, adjustable wrench does the best job, the Channel Lock ones are great. I usually use a vise-grip for the lower part, though you have to be careful not to use it too tight or you will chew it up a bit. The purpose made pliers haven't really impressed me, it is difficult to grip them tight enough, which also chews up the lower part some.

For the headset with the cable hanger, it will likely be easiest to adjust it with the brake unhooked, top nut all the way undone, cable hanger slid up out of the way, get the adjustment set with the lower part and the lockring, then bring the cable hanger and locknut down and lock them in place.