I know lots of folks like Cross Draw for Car Defense. For a Lefty I am not sure this is the best plan.
For Right Handed folks carrying cross draw, you draw the gun away from the Drivers Window, with it basicly pointed in the correct direction towards the threat.
Left Handed Folks might need to experiment with an empty and safe weapon a little to see what works best for them. I think I would prefer a Strong Side Holster, and do a transfer to the Right, Weak Hand if needed.
Accessing the "Cross Draw" holstered gun, weak hand, with the Butt Forward is going to be slow, and clumsey as you will not be drawing with anything that resembles a Firing Grip on the weapon. Probably much less chance of fumbeling the weapon doing a transfer to the weak hand if needed.
Something to think about.