I think the first thing to try is to discuss with the landlord. If you can give good testimony that your cat is not going to soil or damage their property, they may make an exception. Or, you can offer to pay an extra pet deposit fee to convince them.
Otherwise, if you adopted your cat originally, I'd seek out the original agency to see if they can help. And if not, try to network within your own group of friends and family. That would allow you to have an ongoing connection with the cat after rehoming. Who knows, one day, you may move again and be able to work something out where you get to take the cat back!
#General