Being an obsessive compulsive neurologist, I always get a MRI of the brain on my patients with exertional headaches. If it is normal, it gives me and the patient a great deal of peace of mind. I always say, "nobody gives you a medal for not checking the MRI."
You might see if you can get your blood pressure checked after your ride, when you get your headache.
Rising or falling sugar levels can trigger headaches....there are glucometers that diabetics use that can check the sugar level. Perhaps a friend has one.
The posture of a road cyclist's head relative to his neck is extreme extension...so that can set off headaches for some.
I really do suggest getting it checked out. If it all is ok, then 2 advil and some mountain dew (sugar and caffeine) before the ride might help.
Its good that you have a doc and have had a good physical. Its nice to have a relationship established so you can go to them with concerns that come up.