I flew for an airline for many years and still occasionally travel for business. I would be reluctant to have my cavies fly as cargo unless it is Spring or Fall. The extremes of temperature are just too drastic during the Summer or Winter. They might have to sit on a baggage cart out in the elements while the baggage handlers fill their particular trolley before heading for the terminal.
The only airline that permits cavies in the cabin (to my knowledge) is indeed Frontier. You may have to be a bit creative insofar as setting up a route on Frontier from JFK to LAX. I don't know if FedEx accepts live animals, but you might check that out.
@Kelsie seems to have a handle on the situation. I have only transported my piggies for a three hour trip which is a bit different. They don't seem as sensitive to change as one would think......in fact, my boys seem to like car rides so long as they have each other........and me. If I'm driving them alone, they are strapped into the front passenger seat where I can reach in occasionally and give them a pat. If it is only Sparky, he lies on a towel between my legs as I drive and enjoys lap time.