Question: Why would ferritin rise on a low-carb diet when iron status is stable?
Well, they sound copper deficient because copper is needed to mobilize iron out of ferritin. Copper is most abundant in plant foods, except that it's also very rich in liver. And it's pretty decent in a number of shellfish, but on a low carb, steak and cheese diet, not only are you deficient in copper, but you are also now pushing your zinc levels up, which will lower your copper absorption. Low white blood cells is, first thing that I'm going to look at is copper levels, especially if the neutrophils are low. And that would very easily explain rise in ferritin.
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DISCLAIMER: I have a PhD in Nutritional Sciences and my expertise is in performing and evaluating nutritional research. I am not a medical doctor and nothing herein is medical advice.