My suggestions, for what it's worth:
Choice 1) Store bikes inside vehicle if at all possible. For a 2300-mile trip, you've got to stop sometimes and it will be nice to know your bikes can be locked up inside. Plus, they are fully protected from the elements. Provides maximum peace of mind.
Choice 2) Store wheels in vehicle and mount frames on rear rack. Point the frames in opposite directions and they will nestle together nicely. We would tie old tube socks around the frames where they might contact each other or anything else and then tie it all down securely with a bunch of rope. No shifting over bumps and reduced exposure to wind, bugs, elements.
Best wishes on your trip!