Hopefully you get one soon, OP! I wish you luck, I mean it, really. You are very responsible with your cats and thank you for keeping them with you, and I understand that it is very frustrating situation.

I was in your situation couple weeks ago. My landlord kicked us out and only gave us just lil bit amount of time to move out. We used Zillow and contacted more than 20 apartments and only 7 of them got back to us and by the time they got back to us, sometimes the landlord has already accepted other application. We had luck after 3 weeks.