Athena has a LOT of different tests for Peripheral Neuropathy. They have a financial program that may help you with the cost if your insurance claim is denied.
Athena Diagnostics - Athena Alliance Program
You can get a "Letter of Medical Necessity" from them to include with your first request for pre-approval, or with an appeal of any denial.
Athena Diagnostics - Athena Alliance Program
Call them up and ask to talk to their Patient Services Department and ask about how they can help you to get your insurance company to come through for you. I've had dealings with a few different specialty testing companies and Athena was the most expert and interested in handling insurance issues.
For neuropathy, they offer many more tests than CMT testing. I think it was this panel that my doctor ordered when I was first diagnosed.
Athena Diagnostics - Sensory Neuropathy Evaluation
It tests for four conditions, and ALL of them have some level of treatment available -- that seems to me to be a key factor that an insurance company should look at when deciding whether to cover a test. (A positive result for a SCN9A test, on the other hand, doesn't lead to any effective treatments yet.)
Though it's a little difficult to navigate, their complete test catalog is here.
Athena Diagnostics - View Full Catalog