Then don't use Mozilla's server.

(There's a tough choice here: Persona's crutches make it much easier to deploy incrementally, but there's no incentive to ever get off the crutches and people think that the crutches are Persona.)

BrowserID requires nothing from Mozilla. They of course offer a public server so that you don't have to run your own server if you don't want to, but it's entirely, 100% optional.