I have been adhering to what you could call a "Paleo" diet for about 4 months now while I work on healing my gut. I do eat oils (coconut and olive), organic fruits, veggies, and meats and fish. I am grain free, with root veggies (parsnips and carrots) on occasion).
I can ONLY tolerate fruit first thing in the AM on an empty stomach in the form of fresh juice (with a juicer) or whole, depending on the fruit. I take Enzymedica CarbGest or Digest Gold with everything I eat.
Today I tried to eat some fruit in the middle of the afternoon (with enzymes) and was hit with a terrible headache akin to the headaches I used to get after most meals before I altered my diet.