Just wondering if this process will stop the insurance companies from telling me how much I should be paid.
The contract with the property owner is independent of the insurance estimate. That having been said in most instances in which the contractor is involved in a project following an insurance claim, when the insurance company is paying for the work, the scope and cost is consistent with the insurance adjustment; therefore your contract price for the same scope of work would typcially be for the same amount as the insurance adjustment. You have the right to set your own pricing for the scope of work but most property owners expect the work to be completed for the value of the adjustment because then the property owner is not spending any of their money. If there is an additional scope of work beyond the insurance adjustment, that scope must be clearly set forth as well as the associated cost for that portion of the contract. That will avoid misunderstandings with the property owner.
Most property owners have the expectation that the insurance proceeds will cover the full scope of work, including permit fees/expenses. Those items, such as permit fees/expenses as well as scope of work impacting the contract price shoudl be brought to the attention of the property owner, or with the authority of the property owner, you can review with the insurance company. The basic point is clarity, so that if the total value of your contract exceeds the insurance proceeds, the property owner understands they will be required to pay any balance from their own funds. Having this discussion and the related transparency should avoid payment issues on the back end, lien issues etc.