The proper way to restore it with the unoriginal bigsby is to remove it, find whoever installed it in the first place, then proceed to pound it into their skull repeatedly until it turns into dust.If the Bigsby was original to the guitar, it should remain,
but it wasn't. It was added sometime later. So if you are
reconditioning the guitar, I would bring it back to it's original
configuration.
I would rather they sold the guitar "as is", most buyers would
have a preference for who was reconditioning the guitar.