Is the mover's insurance company getting out their checkbook? If they are ready to settle this you need a consuting arborist to put a reasonable value on the tree. If you are going to have to fight this in court you need a lwayer to determine what measure of damages your state allows. IT might be "value to the house" as you say, or might be a value separate from the land and house. That detremination will tell you if you need a consulting arborsit-tree appraier or a real estate appriaser or both.