Where are you? I just checked the 2 largest rescues near me...8 at one, the other has 23. I'm sure there are more not on the websites.
I had to stretch my net a bit further than those 2, and went county wide. I suspect small rescues might be better as they may have no staff and need to rehome quickly. With small staff/volunteers, they are also trying to do everything at once...collect/deliver cats, assess them, get necessary vet checks etc.
I'd say contact and register interest to as many as possible. Stress all the positives of you being a cat parent, plus any experience you have. Pester them...call every week.