As a small business owner, you need your money. You also need the goodwill of the community. Good customer relations versus the profit motive is an ongoing consideration. Why not call the insurance company and encourage them to do their job? Here in Washington, we can go online and complain to the insurance commissioner easily. It may also be possible to sue the insurance company for bad faith in the insurance business.
[If this information has been helpful, please indicate below. Please note: I'm only licensed to practice law in the State of Washington. This communication does not constitute legal advice, nor does it form an attorney-client relationship.]
That depends on what your contract with the customer says. If you do have one, it may not address the situation of waiting on an insurance check.
You damaged their floor, so it was your fault that they needed an insurance claim in the 1st place, so you may be stuck waiting for them to be paid before they'll pay you. It seems they've at least affirmed their obligation to pay you what they owe you.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.