I just sold a Haunted Woods map piece for about 5 or 6k. Unfortunately, there doesn't seem to be one
rare piece that goes for much higher for the HW map.

The snipers tend to randomly assign a random map piece a much higher price, but that might not work if you only have a single piece in your store.
And I vaguely recall non-rare treasure map pieces going for 20k or so. You might want to check the Shop Wizard for an idea of pricing: look for shops selling multiple copies of the same piece, as they tend to have the other pieces as well. Then you can find your piece's price, even if it's not the piece the shop wizard wanted to give you.

Unlike the HW map, Treasure Map pieces
do have expensive rare pieces (they're usually corner pieces, I think).