Check out the Cavalari setup sheet. It's a lot of work, but it's what I'm going to try first.

It's weird that your battery is all the way forward and the rear is still planted and nose still lifts so much. Again, I'd go over the entire truck and check your brake settings on your esc.

Thinking about it a bit more, that's a lot of horsepower. You probably should be letting off before the truck is leaving the face of a jump and def using the brakes.