For clarity, what is your contract like? You mentioned you are hourly so I assume there was no formal project contract? As you say, you were on the home stretch of the project and it is they who decided to start a new one by changing the parameters, so I would personally approach it that way, which is a bit different an issue than simply 'an employee that wants to change everything'.
I work in the office and get pay by the hour. So thats not an issue. I'm getting pay for, it's the principle of the matter. I don't want to work on it forever just to get the design finish. There is no point on my part and theirs. I will also get burn out and would no longer want to design websites anymore. :-/