I no it's easy for me to say but please don't give up, there's got to be something that will work for you. My regular eye doctor was reluctant to recommend me to a contact lens specialist because he was sure the lens would stick to my very dry eye. He told me to not even bother making an appointment unless the specialist read my history and thought she could help. The long drive doesn't help matters but hopefully it will pay off soon. It could be the type of lens or the fit. Perhaps Sara's idea will work. Please keep trying, would hate to think there's something out there that can help you but you just don't know where/what it is.
I have two dogs one I like and take care of because we have her, the other I love, so know what you mean about your cat!
Take Care, Jill