Ah, sorry for late response, I am currently working away from home on nights
Hmmm, I'm afraid the deaf cat coming up to your dog and them seemingly getting on may have just been a fluke
We currently have a dog and two cats, The older cat Rosie tolerates Rocky, but that's about it, Rosie will even sometimes tag along when I take Rocky for a walk (which may look funny to people who don't know they live in the same house, but I don't like it when she does this as the roads may be busy
)
Ruby, on the other hand, just turned six months old. They get on most days and kind of understand each other's body language—well, I think they do. They will chase each other in turn, but as for snuggling down and sleeping together, Rocky, who is a Lhasa Apso, still freaks a bit if she jumps up next to him on the settee. If she lies down, Rocky will get up.
As for you, well yes, certainly a kitten would be the best way forward, but there is never a guarantee that any cat (deaf or not ) will accept the company of your dog, I've had both Boys and girls through the years and to be honest, they were all clean, never any issues, our current cat Rosie doesn't even use the litter tray on a regular basis, who knows where she does her business, hope she's not upsetting the neighbours
Good luck with your searching
It's such a shame, this forum used to be very very busy, pretty sure someone would have been able to help you quickly, a lot of rescues too, social media kinda screwed that up.... I'm just as guilty
others is also a purr's in our hearts facebook page