If you are having no bowel changes, and the headaches come back without the salt, it sounds like a no-brainer to me. For some reason your body needs that much. We have been told over and over that salt is bad for us, so it is sometimes hard to wrap our head around high doses.
As I was reading your post, I wondered if you need the Sea Salt for the minerals as well. Perhaps try taking some blackstrap molasses each day for a couple of weeks and see if that affects your need for salt.
Also, are you having mucus problems? My cousin needs high doses of salt to keep those problems down, otherwise she is in the hospital. Just something to think about.
I am all for listening to my body, no matter my doubts.