Going back to the "old Navy days", if we had a board we needed to repair, it went like this:
Map where the runs are
Excavate (remove) all burned portions of the board - don't want any carbon that can unexpectedly conduct
Bevel the edges on both sides to allow the epoxy to have a better bite on the original circuit board
Put a small piece of glass or something flat on board to make a stop - You could probably use a stiff tape
Mix two part epoxy, grind up a same color matching trash circuit board and add to epoxy to get a matching color with original circuit board
Fill in hole - make sure there are no air bubbles in the epoxy (Likely not needed in this case) Make sure board is completely level
Grind up a same color matching trash circuit board and add to epoxy to get consistent color
Allow epoxy to set (Bake if needed for extra hardness)
Remove flat pieces
Grind (sand) and polish area, making sure its flat
Install eyelets and runs
Install components, test circuit board

In this case, you will likely end up filling in the hole with epoxy and run wires to where you can meet back up with the runs on the circuit board.

Just worthless info - we used to have to do this on multilayered circuit boards - nothing like finding out you forgot to install a run two levels down after you're done.