I somehow feel this wouldn't work in negotiations especially when the other side is not playing fair. When they offered as low as $250 it tells they are playing it mean. All this nice idealistic talk is not going to move a blade.
I would suggest don't work on their sympathy or expect them to value your efforts. They will not. Be ready to lose the meagre amount and play it hard. If you lose, make sure it costs something for them to fix their bargain of $250.