Doesn't seem like a huge problem to overcome with a solid plastic overlay. Just drill your overlay to position the buttons where you want them, but as close as possible to the position of the current holes. Anyplace underneath where they don't line up perfectly, you can use a grinder just enough to give them clearance. As long as the holes aren't so large as to prevent the nuts for the button from making solid contact with the panel (be careful you don't do this) the button nuts will screw down tight and not move. If you do it right, it will still look perfect from the top side.
RandyT