I would love to help, I can go from LA to Phoenix or Phoenix to Albuquerque. But, if you dogs won't survive in the cargo hold of a jet, then I'm not sure they would survive multiple hops in small planes. You realize that you will also have to arrange for someone to watch the dogs overnight at each airport they stop at? Small planes cannot handle weather like the big ones do. We also have mechanical, and pilot health issues that could strand your pets somewhere halfway in between. The airplanes are generally small, noisy, not pressurized (less oxygen), and rougher riding. That trip would likely take 4 days between different pilots, even if you can find pilots to do all the legs.
I think Pilots N Paws has a web page with commercial airline volunteers who will take your pets with them (in the cargo hold), but they will be traveling with someone to look after them. While cargo holds sound bad, they are heated and pressurized or they wouldn't allow pets. Five hours on the jetliner would likely have a lower chance of harming them.
just my 2c