Not that I have it down perfect, but I have found I basically need to drink water all day to fix my dehydration and headache problems... I am 145lb 5'10" male and I believe I need about 8 liters per day or Im dehydrated... Especially if your eating all those medjools and cooked food I'd bet you need a LOT more water... I believe I heard durianrider say, "if you eat a cooked meal, it uses about 2 liters of water from your body just to process it", plus if you are exercising that much I would seriously try doubling your water and see how that works for you, cycling we need about a liter per hour... I am able to nab the headaches pretty quickly with water. Try it out!
I remember feeling this way in the beginning. You say that you came from a high fat lifestyle. Now, I'm just making this up, but I am basing it on what I've learned over the last year. So, your body is releasing stored fat into your blood stream which is teeming with loads of sugar from your meals. The fat is messing with proper sugar absorption into your cells so your blood sugar is being maintained at super high levels and may be causing the lethargy/malaise. I'm a math teacher who has been doing this for not even a year...so definitely don't take anything I'm saying as hard and cold fact. But it could totally explain the symptoms. For me, they've subsided completely (I was coming from a higher fat processed vegan diet...so it may take a little bit longer coming from an animal protein diet). Either way, I hope (and I'm pretty sure that you will) feel better soon. Also, I second what Richard said about water...in the beginning I didn't even realize how dehydrated I was until I started carrying around and stashing bottles of water in my car and my classroom and my gym bag. Being fully hydrated definitely made me feel a lot better.
That is a lot of dates and dates are dehydrating make sure to drink water with them, for every 2-3 dates you should have a cup of water as if it were fresh fruit it would have that much water in it.
when exactly during your day do you experience these symptoms? does it happen during or after a workout, upon waking up, when? this may help to pin-point the cause.
also, do you feel you're sleeping adequately? it seems that not everyone requires the same amount of sleep in order to feel good, but i personally do best sleeping 9-11 hours per night.