I just stumbled on a recommendation from Bill Carr for 1-866-SLABJACK. Looks like they are able to do concrete lifting and repair so it doesn't all have to be trashed? Might be worth a look.
Northwest Rock and Concrete Demolition has some good reviews on my neighborhood page. We have a lot of people in our neighborhood who have tree roots damage their concrete and this seems to be the go to. Good luck!