I've seen an endo for years because I'm hypothyroid (Hashimoto's). Not sure what they would mean by "deeper" thyroid testing but this may not a bad type of doctor to see. They deal with anything hormonally related. There are many conditions that can cause neurological type sx if hormone levels are off and at least a few of them are on the standard list to rule out when testing for MS. While my endocrinologist is not an MS specialist, he certainly has an understanding of auto-immunity and he's shed some light for me on several things. At the very least, you'll have another set of eyes and ears on your case. You never know what might come out of it, even if the root of the problem is not endocrinological. Here's a brief overview of the endocrine system:

http://en.wikipedia.org/wiki/Endocrine_system