WYSIWYG:-
Regarding your dog's eating habits, I have had a similar experience with a dog so perhaps I may be able to offer some suggestions.
After many months of dog weight-loss and many trips to the Vet, stool (turd) samples analysed and blood tests, eventually the dog was diagnosed with partial pancreas failure.
As you probably know, the pancreas produces insulin, which regulates blood sugar, and the digestive enzymes lipase, protease and amylase. These last three enzymes are responsible for the breakdown, respectively, of fats, proteins and carbohydrates into substances which can be assimilated through the gut wall, into the blood stream and thence nourish the body.
It might be an idea to ensure that your Vet actually HAS done these blood tests at a time when the dog is either off its' food or when it's eating ravenously. If it is off its' food then it might be in pain and when eating ravenously it is probably starving, as any food eaten will pass straight through undigested, affording no nutrition to the body.
Usually the production of insulin will be unaffected, so the dog will not be diabetic, although it might be as well for the Vet to check for this at the same time.
If partial pancreatic failure should be the cause of the dog's problem this might account for any irrational behaviour in the dog. Poor nutrition can have wide-ranging effects, not just on the body with vitamins, the lack of which caused diseases such as scurvy, rickets and night blindness, but also on the regulation and production of hormones which control behaviour.
Studies on young people with a poor diet show that problematic behaviour such as lassitude, aggressiveness, Attention Deficit Hyperactivity Disorder and other anti-social attitudes can be greatly modified by a properly balanced diet.
I am not for one moment suggesting that there is fault in the way you feed your dog, just that there is a strong relationship between diet and health. If your dog cannot digest the food you give it there must be an effect on its' health.
In particular, it has been shown that if a diet is short in one particular element, usually a "trace element" needed in only minute quantities, the body will ask for some food containing that element. Hence our cravings for particular foods on occasion, especially during pregnancy or recuperation from accident or disease. A dog cannot ask, only by displaying that need as being "picky" over its' food.
If it does turn out that your dog has a pancreatic insufficiency the cure is simple. Your Vet can provide you with an enzyme in powder form that you mix with the dog's food. However, you may find you need to try various makes before you find one that is suitable for your particular dog. In other words, some makes will have little or no effect on the dog.
The reason for this is that all enzymes in the natural state are made to either a right-handed or a left-handed form, i.e. like a pair of gloves. One form will work while the other, although appearing to be a similar molecule, will not. As an example, Glucose, a natural sugar, is a right-handed molecule (D-Glucose, or Dextro-Glucose) while Sorbitol, an artificial sweetener, is the L (or Laevo) form. Both sweeten tea or coffee but a large dose of Sorbitol (L-Glucose) is given by medics to empty a person's bowels. This it does with remarkable efficiency!
I hope the above is helpful to you and to others.
Colyn.