IANAL, but off the top of my head, you should invest in some sort of lockable container, tucked behind the seat, bolted to the floor, etc.
OH's rules for licensed transport require that you wear the weapon, on your person, in a holster, and in plain sight.
Failing that, a locked "steal me" box in plain sight, or a locking glove box or console. Nobody's sure about a locked compartment under a seat (some Chrysler products). "Case" is the word used for the "steal me", so about anything that can be locked is acceptable, and it doesn't have to be bolted to the vehicle.
HOWEVER, if you haven't got a valid license for OH it has to be empty, in a locked container, with the ammunition stored separately. (There appears to be no rule requiring magazines be emptied, just not in the same container as the gun.) The container has to be essentially out of reach of the driver or passengers.
I have a three-compartment range bag. Two of the compartments are lockable. The third isn't. Placing one or more empty weapons in the locking compartments, and locking them, with the ammunition in the unlocked compartment, should be fine, as long as the bag's locked in my trunk.
If I don't have a trunk, it'd have to be behind the seats in a pickup, for example, or in a toolbox. I'm not sure you'd need to put that bag in a lockable compartment behind the seats, since it's a locked case, but it'd be pretty dumb not to have a lock on the toolbox.
If any of this makes sense, I apologize. If the vehicular carry rules seem strange, I didn't vote for most of those guys....
I think that the OH rules for unlicensed transport probably are valid for FOPA purposes in any state, but some states don't want you to actually stop in them while transporting a firearm. Stay out of New York....
Regards,