I've since found five causes of my headaches, though I doubt anything would have turned up on an MRI.
Sinus pressure. Sinus headaches are behind the eyes, in the cheeks and sometimes in the upper teeth. I take Sudafed PE for these, as often as directed. Acupressure at the points beside my nostrils helps, too.
TMJ. This can feel like a sinus headache. If relaxing my jaw for a few minutes helps, I know it's at least partly from carrying tension there. I put in my splint, take ibuprofin, and do my best to relax. Although acupressure helps some people with TMJ problems, I've never found it found it useful for that problem.
Neck pain. These can be from either misalignment of the spine or neck tension. I tend to feel these on the top of my head (tension) or near my neck (misalignment). I do some neck stretching and try to get my neck to pop. If I wake up with this kind of heachache, it's usually because I need to prop up my pillow by putting a towel under it. Acupressure at the point between my collar bone and shoulder blade, and gripping my neck muscles both help; so does massaging my neck.
Hunger or fatigue. The hunger headache is easy to fix, but if it's fatigue, I just have to slog through the day and drink high-octane tea (English breakfast). I've had fewer fatigue headaches since I stopped staying out until 11 pm on weeknights.
I take ibuprofin for all of these headaches. I don't wait for the pain to become intense; it's better to stop them early than wait for muscle spasms to begin.