Two comments.......That is an exceptionally long distance for a general aviation transport. That is likely a far better transport for a commercial flight. There is a link on the PNP home page to information regarding commercial flights.
The airports you list are all typically used by commercial carriers so that might be the best approach.
At the sending end the rescue may have to bring the pup to the closest commercial airport.
Second comment that we rarely discuss, but there are times it needs to be recognized. Flying general aviation planes is not inexpensive. Every transport done by general aviation planes is at the expense of the pilots. Adding to the cost is the fact that for every mile a pilot flies with the animal on board, another mile is flown empty to return home. Using the most inexpensive costs of general aviation aircraft operation I would estimate the flight from Mohave to NYC for one pup will run about $4500 all paid for by the volunteer pilots.