Independent insurance adjuster?

My barn roof had insulation under it. After wind damage my insurance paid for the roof and insulation to be replaced.

The contractor I hired installed the insulation wrong and batts have been falling off into the barn ceiling onto the floor ever since. He installed it paper side up, and didn't secure it to the joists.

He refuses to fix it. The insurance company says because I hired him and they have already paid for. It it's not their problem.

Other contractors have come out and said what needs to be done. (Properly sized batts, installed paper side down, stapled in place, supported by insulation supports.). I am going to sue the original contractor to either do it right or pay for it to be fixed. My original contractor isn't going to take their word for anything. I guess the court will also require something other than my say-so? The photos of insulation falling off the ceiling are convincing but the correct fix is probably not obvious.

Do I need an independent insurance adjuster to look at the roof, verify that the job is wrong, and say what needs to be done to meet professional standards? How do I find and hire one?