I'm really glad you posted this, carnivorous, as I too am searching for this answer. From what I have found the liver can only handle around 400g of protein per day. And the ability to process this amount probably slows down considerably before it reaches this amount. I think it is likely that you slowly built up excess amino acids in your blood over the time period of being carnivorous.
It takes quite a bit of amino acids to get into hyperaminoacidosis. There is a poster by the name of redfulcrum, who did a very dangerous experiment getting around 1000g of protein per day and reached this state of amino acids very quickly within a couple weeks forcing him to the hospital. You might have just experienced something similar, except with a much, much slower build up.
I also feel that excess protein can be one of the main reasons people have problems with low-carb diets although I can think of plenty more, many people gloss right over this. The body has very little need for protein(perhaps as low as 30g/day for sedentary adults) and all excess amounts will be converted to glucose or fat. Saying its the problem for 99% of low-carbers is going way to far, imo. I lift weights intensely and have been eating low protein (50-100g) per day on average and have still been suffering energy wise as well as a host of other issues. The liver needs to be functioning properly to allow for proper fat digestion as well.
I think rabbit starvation is simply getting too much amino acids in the blood which cause a back up in the liver and completely mess up the nutrient composition of the blood. So essentially I'm saying rabbit starvation is hyperaminoacidosis, or they are very closely related.
Thats also very interesting that you fasted for 4 days on nothing but tallow. I think this is a great idea if you had been intaking so much protein. Once your intake to 4-5 pounds of meat which is something like 4-5k calories you are still getting over a 250g a day of protein, which even if you are active is way too much and could eventually lead to the exact problems that you described. I know 250 < 400 but who knows what happens to the liver after prolonged high protein intake. The amount of protein matters here not the percentage. I've seen numbers thrown around that 250g is actually the maximum amount of protein the liver could handle.
Also, for those that are active enough like you, I would suggest, as I have previously that for the more calories you consume, the more should come from fat (or carbs) and not protein. I think this is very important that excess calories do not involve protein at all! So, as you can see in your case that if you do overload on protein, you can actually go for a few days on just tallow for energy with no protein intake. It will take a while for the blood to clear the amino acids. Redfulcrum, took quite some time to reach hyperaminoacidosis, so it is possible to have quite a bit of excess to supply you with your protein needs for the coming days.
Now, a good question to ask, would be whether or not its beneficial to consume extreme amounts over the course of a few days and then fast on fat for the next while? I have no idea, but I think it could work and I would like to try something like this in the near future. Carnivores in the wild go several days without eating on purpose, so its very likely that the have sufficient amino acids running through their blood to cover their daily needs. Although carnivores are better adapted to higher protein intakes and can handle the nitrogen waste, ammonia much better than humans.
Interesting thread - let us know how you are doing.