Well at least you've braced for that in case it happens, but hey you never know, you might get a good diagnosis out of the deal. Especially if this neurologist is a headache specialist. It's unfortunately true that regular old garden variety neurologists are thought of us as often being ill informed regarding CH.
I bet you've seen that this is indeed some straight up classic CH behavior.
I've known some diagnosed CH'ers that mainly get hit in the temple (upper trigeminal), as opposed to the behind the eyeball routine I got used to thinking of as the CH standard.
It sure sounds like how a cluster cycle often ends - CONGRATS ON MAKING IT THROUGH, and now hopefully you'll gain a nice long remission.
Yep - all they can really go by is a description from the patient, and your descriptions seem fine.
Best of luck and results with the upcoming appointment. I'd say don't make too big of a deal out of it - if the doctor isn't right, just set this as another appointment/doctor to ignore, and seek out a headache specialist while you're in remission. They can have long waiting times, but you don't have to be in an active cycle to go in and get a diagnosis.