When I was actively working with rescue we were also a network of foster homes. We did something we called a "sponsorship program". Since, as you know, being at capacity doesn't mean you can turn them away. Most people want the rescue to take in the animals that they find or can no longer care for. We always had to explain that we didn't have a shelter. We found that through our "sponsorship program" people were willing to be the foster for a particular animal. We provided the vax and spay/neuter and would provide food if they couldn't. The sponsors would bring the pets to our adoption events and they were advertised through our rescue. Just a thought to maybe create more space... we found a lot of people were willing to care for the pet in their home with vetting and help finding a forever home.
You are doing an amazing job!
You are doing an amazing job!