Well, almost as quickly as I made my list of possible causes, my headaches faded away. The few things that I changed: 1) got back on Alpha Lipoic Acid and 2) adjusting my basal insulin. I'm still seeing some unpredictable things happening with my daily BG, but it's not as consistent and not accompanied by a headache every day.
I am happy to say that I've been having tea and cider every day and it seems to be a non-factor. This week my time spent in the school building was limited, but even the days I was in all day, I didn't have headaches. It's only been about a week of good fortune, but it seems like it's going to continue.