I assume you're using Robart "Hinge Point" type hinges.
File or cut away a 1/4" wide clearance notch in the beveled surface so that you have a flat surface to start your hole on. To keep the hinge gap as tight as possible, you will need to recess the hinge anyway, so why not make it work in your favor?

If possible, it's a good idea to cut/drill the hinge slots/holes BEFORE the control surface are bevelled.