Trigeminal nerve pain can be triggered/worsened by an enlarged vein pushing against the nerve at just the right spot. Cannabis causes hypotension via vasodilation, hence the potential trigger.
The thing is, veins don't grow perfectly parallel, which means hypertension can also cause pain via vasoconstriction, if the vein slightly spirals around the nerve and also constricts; think like a snake wrapped around an arm and squeezing. So it's possible both localized vasodilation and vasoconstriction are causing these headaches, considering the times the headache is worst ("cannabis use or after waking up) and mild but constant (after stimulants like caffeine).
If your pressure is a bit high during the day, a very small dose of a vasodilator drug taken after your medication would normalize it and that would, hopefully, stop the pain overall. You could still have orthostatic blood pressure issues too, but certain mild exercises can help with those too (assuming there's no other underlying blood flow issues).
But there's not enough data to say conclusively, hence taking your blood pressure as directed, as well as throughout the day sitting (after sitting at least 3 minutes without moving much) to see if there's any abnormalities with it, as well as the orthopedic pillow. If the pillow helps it also narrows down the cause.
That said, if it's the trigeminal nerve and you can't control the veins there well through medication... Good luck I suppose. Most surgeons won't want to cauterize because of mild (yet constant) pain. Acupuncture could achieve the same result, but that would be a scary gamble, because there's also potential they hit the nerve wrong with the micro needle and instead worsen the pain. That would be a last result solution, assuming it's the trigeminal nerve causing you issues.