I have not spied a G8 in JAX although I was a second too late for a Grand Prix GTP about 3 months ago. On the aisle at JAX, you go to the parking garage and have to collect keys from the window located there (as they have no gates at the exit). Only takes a few minutes longer and they usually give you the option of what is available. I've driven Volvos, Avalons, Auras and the like there.

You have almost no options to assure yourself of a G8. I think they are premium in Florida but sometimes considered "special" and kept seperately if available at all.

Good luck!