Hey delta,
I was looking for the single-flute pilot countersink bit you mentioned, but can't seem to find it. Looking at Avery, Brown, The Yard, they all seem to have three-flute pilot bits.

Do you remember where you found yours?
Maybe you already have this figured out, but, here's my thoughts for what it's worth. I also used the Vans method (install nutplate and use that to guide the pilot).
I found that the countersink starts with some guidance from the original hole. Then as the countersink gets deeper, the pilot has nothing to guide it and the cutter starts getting a bit loose. Finally at the end of the cut, the pilot finds the nutplate and guides it home and all is good.
I found it's that middle part of the cut where you have to have a steady hand. It doesn't have to be perfect to the micro-thousands of a nat's whisker, because the end of the cut, which has the nutplate guiding it again, will clean up a little wobble. But, if you get too sloppy in the middle, and let the cutter move sideways or at an angle then the cutter can put in ripples that are too deep.
Once I figured out what to pay attention to, it was pretty easy. Just grab a hold of the micro-stop with your free hand to keep it from moving sideways and to keep it square ... watch what you're doing through the micro-stop's window ... make a slow-turning steady cut ... keep in mind you're free-handing it in the middle of the cut.