Potential treatments you didn't list in order of decreasing plausibility: amitriptyline, nortriptyline, magnesium (OTC), coenzyme Q-10 (OTC), zonisamide, ACE inhibitors, ARBs, pregabalin, feverfew (OTC), bupropion, verapamil, valproate, memantine. Many of these are bread-and-butter drugs for internists, GPs, and family doctors -- no neurologist needed.

For doctors, a headache specialist at an teaching hospital can be a good choice. They tend to be knowledgeable and persistent.