Something I meant to mention at the end of my post--while I got those electrolyte problems the first time I did induction, later on after that first failure, when I tried eating the same way again, I was fine.

I don't think an Atkin's style diet or even a slightly more ketogenic version is necessarily deficient in anything. At least not compared to a higher carb diet. Most of the foods that are removed aren't all that nutrient-dense in the first place, unless they're fortified.