Working the front-plate myself

A manual punch is much more accurate than a step drill. Most step drills have a single cutting edge and thus are not balanced! (Most will not really cut a true round and dimensioned hole.) If a step drill is all you have to get the front piece hole and the back piece to match, you can try a three piece sandwich so the the step drill will cut the right size hole in the front and back at the same time. The middle of the sandwich should be something like a soft wood of the right thickness to get the effect. Then the issue is making sure your drill bit is truly perpendicular to the work. Not as easy as it sounds.

More importantly do you have the same number of fingers after you finished as you did when you started?