Here's what i'd do...
Use a piece of Velum, a see through drafting paper, and tape it to the face. Use a hard flat graphite or Crayola and rub the face that is remaining so it transfers to the back side of the Velum. Now, flip it over and locate it so it blends symetrically with the existing design... BAM!!
You now have a complete pattern to work with.
Now you can saw off the split portions and I would use a horizontal line to cut to. This will make it much easier to add another piece to carve the design into following the suggestions above using a Dremel. Someone who carves duck decoys would be of assistance or other miniature figures.
You can trace the carved V groove with a soldering iron or woodburner to get the wood a little darker like the original. Laser etching is another approach and they can digitize the remaining pattern and recreate it above and then etch it in on your replacement patch.... $$$..... I donno?
If this is beyond you interests or capabilities, then the choice becomes... sell as is or
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)