I admire what you dog pilots are doing, dog lover myself. But I have to wonder why this is necessary. Can't these dog people find homes for the doggies closer to where the pups are? Why are they able to find homes a long way away but not locally?
I have visions of two plane loads of dogs going in opposite directions and simply exchanging one bunch of dogs for another.
As Paul said, it's effectively all one-way. The overpopulation issues are in the south, and the need for healthy, adoptable pets are in the north. This is mostly due to culture and a bit to climate. In the south, people don't spay and neuter their pets nearly as regularly. In the north, it's done almost universally.
There's also the climate. You have significantly more stray dogs in the south, which aren't spayed and neutered and thus increase their population. While dogs certainly can survive northern winters, you don't have as many. Plus, I think animal control in the north typically does a better job of capturing stray dogs. The flights south are the dead-head legs, the flights north are full.
Sometimes Florida can be both a sending and receiving state, but even then it's pretty rare. I've had transports to Florida, but they were usually high-profile transports such as when an animal testing lab in North Carolina (a sending state) was shut down and I flew an Aztec full of beagles to Florida. I've also gotten requests of sending dogs from Florida, but those have rarely panned out. You'll sometimes have specialty breeds, for example greyhounds are typically in a few states where greyhound racing is still popular (one of which is Florida) and then go to rescues around the country that specialize in greyhound adoption.
I've only once had a trip where I had dogs going both ways, but even that made sense. I flew a bunch of large dogs that were older and generally considered unadoptable to Best Friends Animal Sanctuary in Utah. I then went to LA and flew 47 chihuahuas to New York City. In both cases, it made sense. Best Friends will take in animals that are generally unadoptable, and then California has an overpopulation of chihuahuas (which became popular in NYC and SoCal after "Legally Blonde" came out).
I didn't understand the need until I got into it. When I was working with some contacts at the ASPCA a few years ago, they said that they did the math and determined it is possible to end euthanasia with transports. However, the catch is logistics (both transport and pairing the senders/receivers) and funding the operation. Realistically transports will never save them all (millions per year), but it will save the ones it will save.