Gunny sounds a lot like our foster Ferrall, also not a pit bull, but a standard xolo. He wants to eat our cats. I have tried over and over to desensitize him to them, and it doesnt fly. One trainer collegue suggested the same thing you did, that he may have already experienced hunting/killing a cat and that is why he is so obsessed. He likes to say Ferrall is very bite confident, because he will without hesitation pounce on any cat or unkown dog. However we can get him to warm up to new dogs with a lot of time and patience, and he plays very nicely with the dogs he in our house.
Ferralls breed is known for being guardy and while hes not over the top, I do sometimes worry that when he gets older he might become even less tolerant. Right now Ferrall tolerates strangers pretty well, he cans ometimes be aloof, and has a few times been very alert/ guardy around suspicious looking people, but overall is good. Children are another story, Ferrall barks and lounges at them. He doesnt do it everytime, but hes done it enough times that do make me uncomfortable ever trying to properly introduce him to a child. let alone LIVE with one.
Ferrall is also a one person kind of dog, he and i are so bonded we have a great relationship and he tries hard for me, my partner on the other hand Ferrall couldnt care less about what she says or does. We both feel that if she did something he didnt like he wouldnt hesitate to correct her...with his teeth.
I love Ferrall a lot, but i do sometimes feel like i'll never be able to place, and i do worry about the stress i am putting on my family and when it will be too much. My cats are not happy, especially my very sensitive manx, she wont leave my bedroom because shes too scared, I had to bring her to the vet and get her anti-inflamatories because of what the stress is doing to her body and my soul mate Mr. P has been pottying outside of his box, and has been generally very iritated. My partner doesnt trust him, and has asked me more then once to return him. I just dont have the heart, the rescue who hes through cant handle him, none of the foster homes are experienced enough to deal with him, and they will not transfer him to a rescue dedicated to his breed with the experience to work with him, instead the president of the rescue offered to take him back and send him straight to a training facility for a minimum of thirty days, that uses aversive training methods. I can't do that to him. its not right, it would hurt my heart to its core.
I keep praying that i can find that breed experienced home, without cats, or children, outside of a city. its probably been around six months and we've had no luck, if it were just me I'd keep Ferrall for his entire life. I truly love this dog, but when it comes down to it i have to pick my family over him, and if theres ever an ultimatum given to me, i'll be all out of options.
anyway, not to make this about me. geez sorry. i just wanted to let you know that i truly sympathize with you, and i hope that you can hang in their long enough to find that perfect home, just as much as i hope my family can!!