any chance given the style of lantern pinion you are trying to make to do all the drilling on two plates soldered together as a stack, then separate them and cut them to final round shape?
I've used this method many times when trying to make plates or discs with identical hole locations. I usually drill an extra smaller dia hole to act as a reference for aligning the finished assy and get the holes assy'd in the same order they were drilled.
For the drilling itself, I'm assuming you used a centredrill first, and are using good quality twist drills?