Back when I used to work freelance, I learned that all my contracts needed to have a provision not releasing IP rights until final payment was made. This provides the legal stick to side-step going through a commercial contract dispute. You frequently run into companies wanting to pay fractions of amounts due and not having a strong incentive to hurry along a resolution. Instead, without IP assignment it becomes a copyright enforcement action instead and that can get attention and resolution much faster. I never ended up needing to use it, but I did have to remind a few customers that the provision existed. This all came out of a client stiffing me on a large bill that was, at the time, extremely damaging to my cash flow.
With the above in mind, publicly changing a customer's website to something like this is *highly* unprofessional. Better to simply force the site down in a legal manner that conforms to a signed contract.