I do so wish I could be some real help to you. But I don't know enough about Cushing's. I did a little research tonight, but only came up with this dietary recommendation: high protein/low fat/low fibre/low purine. Something like fish, rabbit, green tripe, might be useful if this were the case.
Now, considering your dog has excess protein, this doesn't figure really....
So do try and post your question on the "Ask a Vet" forum. You will eventually get through, even if you have to keep trying. One of the vets there might be able to help you.
You might try " The Honest Kitchens" dehydrated foods. They have several varieties you can read about. Though their ingredients are top of the line, some of their varieties have a higher carb count or higher protein count than others, so pull it up on line and read the carb count and protein count for each one. "Embark" is their highest protein, so forget that one. "Preference" is a veggie/base mix that you add your own meat too, so you'd have the most control over protein count with that one, since you'd be adding the raw meats or soft boiled eggs or whatever, yourself.
There's no such thing as a food with NO protein, at least not one that will healthfully maintain a dog for its lifetime. Do a Google search for "diets, renal failure dogs" and you will come up with a wholle host of websites that have recipes for home cooking for dogs with kidney issues. This is what you need, since dogs in renal failure need as little protein as possible in their diet because their kidneys can't process it. There has to be SOMETHING on there that your dog will eat readily that your vet will agree is safe for her to eat every day. The Hills K/D is their kidney diet, so as long as she's eating that, it's probably your best bet to stick with that for her main meal, and find something you can home cook as a treat to give her with her pill.
A sample of a meal that contains only 7% protein would be:
3/4 cup raw rice
1 large egg
1 oz. liver
3 Tb sp. bacon fat
1 tsp. corn oil
3/4 tsp. calcium carbonate (Tums)
1/4 tsp. iodized salt
Perhaps a bit of the liver from the above dish, once cooked, can be used to disguise her pill, since liver is one thing that most dogs would happily sell their soul for. If you would like, I can do some research for you and see if I can find you some more easy-to-prepare dishes. Let me know and I will see what I can come up with for you.