I see, that's interesting. Initially sounded like a hair weight issue, so by wet washing it you remove enough sebum to not drag on your scalp too hard. But I'm not sure it adds enough weight for it to do that.
I wonder that over time your scalp produces enough of some chemical to give you a headache, and so you need to rinse it away before that happens? Especially since you mention that any wet wash helps, so the chemicals in the shampoo aren't actually relevant for it. Interesting issue though, don't envy you.