that tree probably has a value MUCH higher than you are thinking
many moons ago the Ladybird Wildflower Center south of Austin had signs on some of their trees especially near the parking lot giving the value of them.....they were much higher than one would imagine especially for nice quality oaks such as yours
in your case that tree will live, but it is ugly and that much damage may well take years off the life especially as it gets older and gains even more value (if properly placed and not bumping into the house or causing other issues)
that contractor is an idiot and probably needs to pay up and will probably feel a lot of pain when he does if he gives you full value for that damage
the one thing I will say is in the "tree unit cost" in the above calculator it defaults to 82, but I am personally exactly sure how that will be calculated I believe it is the cost of a replacement value tree there is info on the WWW, but it does not really give a good guide possibly calling the people that give that calculator could answer that
either way you are probably looking at a 12" to 14" diameter tree at "breast height" and that gets the value up pretty high then you need to figure the "value" of that damage
I think the tree will heal up and be alright, very low chance of oak wilt this time of year but I would still go ahead and have the neighbor pay for an arborist to see it and go from there.
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