I am adding a vote for getting a structural engineer. In my experience, contractors may not be able to judge how extensive damage is until the work is underway.
Was the insurance adjuster hired by the insurance company? I am not trusting the insurance company to tell me what the actual costs will be of repairs. I would hire the engineer, make a list of what should be done, (following corralbrook’s recommendation) and submit bills to the insurance company after work was done. I am very concerned what you imagine to be a very generous estimate for repairs may not cover all your repair costs once you get going.
Sorry to be negative. I have had a building knocked off kilter by wind repaired. It was major.