Her head looks a lot like my Derby:

I call him a lab mix, but honestly have wondered sometimes if he has pit in him because of the shape of his skull.
Obviously, though, if he's MIXED with something I would have him classified as the other part of the mix just to avoid these kind of semantics. I hate insurance companies that do this, by the way. They should base their decisions on the dog, not the breed. I think if the dog can be certified CGC or go through a certified obedience class or become a certified Delta dog, etc. then the insurance company should make exceptions for these breeds and the owners.
So, you are definitely doing what you need to do by getting the vet's opinion. Be sure you tell the vet exactly why you are doing this. Hopefully, he will be sympathetic and skew his opinion in your favor - not lie, of course, but if he thinks your dog is a pit/lab mix, maybe he could write the letter to say your dog is definitely a lab mix, get it?
I think it's very hard to determine exactly what mixed breeds really are unless you know the parents. Derby looks like a lab mix one day, a pit mix the other day and he has double dew claws on both back paws so I suspect he has husky or some arctic breed in him as well (to go along with his slightly bushy, arched tail).
The most important thing is he is an intelligent, docile, loving, playful companion. And, I'm so proud of you for recognizing that moving to someplace that will accept you and your dog is the only decision and rehoming him again is not even considered.
We are here to support you. Good luck and keep us informed.