Do you know a lot of people around the country? I've read about transports (typically for a rescue) across the country. It takes some organization, but if you some people along the way, maybe it could work. You just need a few people who are willing to watch the puppy for a night and make a long drive.
That's what I was going to say.

Since most of your trip would be along I-40, I'd be happy to take the leg across Oklahoma for a tank of diesel. (My car gets 40 mpg). There are organizations that will do this, I know.

Karen