Don, are these Helicoils you are installing? That would mean the studs are 9/16" diameter, so those stripped threads are already at 36/64". My suggestion would be to skip drilling, and just run the tap in, using short strokes and plenty of lube. It will act as a reamer to remove the excess metal, and the hole itself will help guide it.
I've repaired several holes that way (including intake manifold bolts on my Stag) and it's worked great for me. Taking out that tiny bit of metal with a hand-held drill motor is a recipe for disaster IMO, as the bit is bound to grab and twist.
Another option might be a straight flute reamer instead of a drill bit (in a tap holder instead of a drill motor). If you wanted, you could even grind down the edges of the flutes for a bit, to act as a pilot; but then you'd need a second reamer to finish the bottom of the hole.