Not nearly as bad as the situation that you are in, but still pretty damned annoying. Ours is OBSESSED with food, and is constantly on the prowl for more and more. Feed him, and as soon as he lifts his head from the bowl, he's following us around, mewling for more.
We used to put food items that don't need refrigeration on top of the fridge, but he has learned that he can jump that high. He is the JJ Watt of cats vertical jumping. He often eats so fast that he pukes, which is just charming, of course.
Both the insatiable appetite and the vomiting have improved very slightly, as we have taken to feeding him 5 times a day - one helping of high-end wet food in the early morning and at dinner time, and 3 automatic feedings from the dispenser. Needless to say, you can just about set your watch by his laser focus a couple of minutes before each one.
We had to resort to storing bread in an enamelled Dutch oven, and I've caught him weight-training a couple of times, so I'm sure he'll bulk up to the point that he can open that, too. You can't even put things behind a closed door, because all of our door handles are levers, and he figured those out on his first or second day here.
He is so brazen that trying to eat off your plate is a mere trifle - he will try to get the food that's in your hand or on your fork.
He came to us already litter-trained, but he won't use it if it isn't diligently cleaned. For some reason, he pees so much that he leaves clumps in the clumping litter that, without ANY exaggeration, are the size of hockey pucks. How a sleek, in-shape cat can hold that much liquid is beyond me.
He will not even consider not jumping onto the counters, and will sometimes do so while he's right beside one of us. His zoomies are unbelievably energetic. and you sometimes can't even focus on him as he breaks cover, then dashes somewhere else that can hide him. He's not trying to hide, it's just that we have stuff.
So, in summation, while the cross we bear is nowhere near as heavy as yours, it still exists, and whatever problem in one's life is #1, it's still #1 until something else supplants it.
I feel your pain, and wish you the best of luck.
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