I finally did it.
One moment of not paying attention, and the hole I was drilling with the step-drill-bit got larger than I needed...
Ah, I thought, good thing I got the drill that has the REVERSE function on it - this will surely un-drill the hole!
No such luck.
In the end I weld-plugged the hole, and re-drilled it to the correct size this time.
The second thing I learned was the weld is MUCH more difficult to drill through than the original metal.