Sorry to hear you are still missing Jake so much
I guess that dogs needing rescued are often ones that have not had the best of starts, and therefore haven't had the training from puppies that our own dogs would get. So I guess they can't take the risk. Were you wanting an adult dog or could you take a pup? They get pregnant bitches and bitches with litters sometimes, don't they, so maybe you could get a pup and train it from dot? Otherwise what about the breed rescues? Surely they understand that some individuals will be okay with cats and others not?
The other thought I had was that when I used to rent a home, I pretty much always rented a place that said no pets, and I always got them without lying. Saying 'no pets' would put a lot of people off, but given that I knew my dogs and cats were well-behaved, and that I would put right anything that did get damaged, I would go and view the property, and
then tell them about the dog (and then the other dog, and then the cats...
). Sometimes I'd get told no, but more often than not, once they've met you, and seen that you recognise that the house might need a deep clean when you leave and you're happy to pay for that, and so on, then they are able to be flexible. Maybe the same might work with the rescues? Go and see some terriers, and then explain the situation and that you are happy to have the right terrier and work with him, and wouldn't hold the rescue to blame if something happened?
Whatever you try, I do hope the right terrier comes into your life soon