Insurance agents and brokers always carry e&o insurance yes, and sometimes (but not always) insurance companies carry errors and omissions insurance.
It sounds like Mr. Cooper wasn't registered on the policy properly. I believe this would be your and your insurance agents responsibility. You could try to go after the insurance agent for the error but I think the insurance company is in the clear here as they will say it's not on them to ensure your policy is accurate.
I understand that they paid in the past, but I don't know if that is enough to remove your and your agents responsibility to ensure your policy is accurate each year.
I think you're in lawyer territory.