Dry out company charging insane fees- pushing for public adjustor lawyer

Quick rundown of the situation- had an upstairs water leak that flooded the first floor of my home and into the crawl space. Moderate water damage to the walls but the subfloor dried out okay and flooring/cabinets needed replaced

Everything has gone smooth with my insurance company moving through this whole process, the place is already repaired and everything back to normal. My problem is the dry out company that came out for water remediation – they have already been paid 21k for their services and they are claiming my insurance company is falling short on the bill by 23k more.

To me that is absolutely bonkers, they were in my home for 10 days total with their equipment running, and one guy coming to check the moisture level daily. They have things on their invoice that are obvious lies and fraudulent billing to pump the bill up. They claim they replaced all the plastic in the crawl space which they never did, along with some other things that are just raising some red flags. My wife signed a contract that we could be liable for these extra charges that weren’t covered, but they want to use this legal route to get the rest of the money.

They are claiming that we won’t be financially responsible if we go through with this appraisal process and will be happy with whatever they get out of this but I am having some doubts. Anyone have experience in this area on what my next step should be? I have this contract with the public adjustor they want me to sign to move forward but I am having doubts.