Poncho, I have the same problem with my ADH and I finally figured it out after years of feeling dehydrated. I have biotoxin illness or mold illness. My doctor said that 24% of the population aren't able to eliminate the biotoxins from mold and once it builds up in the system it causes inflammation. One of the classic signs is low ADH. There is a whole protocol to follow which you can read about at survivingmold.com

A grain free diet is actually recommended as well, so you are on the right track by eating paleo. I actually have to put sea salt in my water every day to stay hydrated. About 1 1/2 to 2 tsp a day. I also mix Ultima Replenisher in with my water too. I'm taking Cholestyramine to bind to the biotoxins.

Ago there good resource is the Bulletproof executive. He has a whole paleo type diet plan specifically for decreasing mycotoxin consumption in food and drink.

This post is from a while ago so I hope you are doing better.