Jerry...

I do have a couple more questions.
First; how long have you tried to stick it out with the brain fog problem? The reason that I ask is that often people experience this when they are going through carb withdrawal, but if they stick it out through the full 2 weeks of induction without cheating, it usually clears up. If it doesn't, then something else is going on.
Second; how much water do you consume daily? You mention that your ketone levels get high (I'm not sure how you are measuring this, but I'll take you at your word that they're high). The best solution for that is to push the water so that your body can flush the excess ketones through your kidneys. Water intake should be a minimum of 64 oz. daily and most recommend an additional 8 oz. for every 25 lbs. that you wish to lose which for you would be an additional 48 oz. for a total of 112 oz of water (ony water counts towards this total) daily. Another option, and honestly one that I think is a better way to go, would be to slow down the weight loss; slower weight loss would result in less ketones being produced from fat burning. A pound a day is pretty extreme weight loss and your body may simply be telling you that it doesn't like it even if you do. Just because you can lose 30 lbs a month doesn't make it a good idea to do so. It could even be more dangerous to your health than carrying those extra pounds for a few more months.
Third; do you take any supplements on a regular basis? If you are losing a pound a day, most likely you are low on electrolytes, particularly potassium and possibly also magnesium and calcium as well. Low levels of electrolytes can make you feel lethargic with poor concentration, sometimes muscles also feel sore.
Fourth; is it possible that you have a sensitivity to arachidonic acid? This is found in red meat and eggs and those who are particularly sensitive to if find that it can make them feel miserable. The solution to that would be to either avoid foods that contain arachidonic acid or to take fish oil with every meal that contains those foods.

You mention that with low carb you are forced into a high animal products intake. That doesn't necessarily have to be the case. For most people on Atkins, fat makes up the majority of their daily caloric intake at about 65-70%, protein comes second at 25-30% and carbs make up the balance. Atkins is really more of a high fat diet than a high protein one.

Whatever you do, you will need to find a method of getting your weight to a good level and keeping it there. Losing large amounts of weight only to regain it takes a large toll on your body and your health and eventually you'll find that you can't lose 30 pounds a month anymore.