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The subject of intentional breeding or meat rabbits is prohibited. The answers provided on this board are for general guideline purposes only. The information is not intended to diagnose or treat your pet. It is your responsibility to assess the information being given and seek professional advice/second opinion from your veterinarian and/or qualified behaviorist.
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I think a second opinion is a good idea. My vet is a bird and exotics specialist, so your bird vet may be a good choice.
I am editing what I wrote earlier because I just checked in a book I have in a section about head tilt, and the illness that can be one cause is E. Cuniculi. So I would ask either vet to check for that (blood test, I think.) It also says that head tilt can be a symptom of other problems, the most common being ear infections. It may not be head tilt at all, but I'd go for another exam just in case.