We did a lot of this with Katrina dogs.
The city I live in rescued many Katrina dogs (over 100) and found homes for all of them ---- even a Pit Bull who had no eyes.
Besides working with Noah's Wish and the local shelter (which sent vets and transport), several private groups shuttled back and forth to the emergency makeshift shelter outside N.O. to pick up and bring back as many as they could fit into their vehicles. Our club drove down with food and medical supplies and back with dogs five times.
We did just as Amanda explained, meeting volunteers from N.O. in Barstow and swapping supplies with animals, over and over.
This ferrying system is the backbone of many rescue efforts, because in a disaster, the immediate area is either too hard-hit to be able to absorb the suddenly homeless animals, or inundated with too many to handle.
Amanda, your area also accepted and rehomed many Katrina dogs. One retired working GSD who contracted heartworm in the aftermath of Katrina was relocated to NC, and two training clubs here in my town scraped up the money for his treatment. He came through it great and is now living happily with a family there.
As we know, many thousands were not rescued. But the ones who were could not have been evacuated and rehomed without the volunteer transport people.