Another thought, might your current department or advisor be willing to allow an external examiner or reader to be on your committee?
Depending on how far away what you want to study is from what you can at your institution, they might be very amenable to helping you do your project within the department in conjunction with other resources.
I know, for instance, that Baylor's Philosophy Department has made provisions of this sort. And I know several other departments where a large part of a project has been guided and checked by an external advisor.
I've also seen changing programs. It can make you an exceptionally strong graduate student and candidate later, but it most definitely will slow your graduation.