Try fasting for the day before your training, breaking your fast an hour before you train for a small meal of eggs or something similar (protein & a small amount of fat, but not too much) then another small meal straight after training. Fasting after training is a bad idea as your body needs to repair.
Keep an eye on your water in-take during the fast. The headache suggests dehydration - you may be taking on too little. Aim for 500ml to 1000ml of cool water per hour (ignore the nonsense that water should be body temperature before you drink it - it's pseudo-science), but don't quaff since a large amount of water suddenly hitting your stomach may induce the sickly feeling.
You might also find it easier to fast from sleeping - take a look at the fast-5 plan. This works best for me since I train at around 5pm, breaking my fast 30mins before training with a paleo protein shake. Fast-5 mean a daily fast of around 17hrs (inc sleep), and as long as you drink enough water and can keep yourself busy (as my job does) then you won't even notice you're fasting.
One other thing - "palaeo" means different things to different people. I personally adhere to the core principle of not eating "Grains, Beans, or Potatoes, or products thereof" as I learned it when I stumbled across the palaeolithic diet a couple of years ago. If I ever slip I feel terrible shortly after eating, and this is compounded if I'm also training. You may find that, if you follow the definition of palaeo being "non-processed foods" that restricting your intake of GBP may help.