Insert is definitely the way to roll on that screw up.
Definitely use a rigid setup and indicate everything so you can locate directly over where the center of the hole SHOULD BE then clean up with a milling op prior to drilling.
If your intrepid customer screwed up the hole as bad as it sounds, there is every chance the currently modified opening is likely elliptical and no longer centered in the original position. If this condition exists, simply running in the new oversize drill to prep for the insert will result in the cleaned up hole not residing in the proper location.