Hi there!
Yeah, I can think of some ways of doing this! But first, just for me to be sure(I saw your thread), try to change the offset of the car sprite with my plugin. Make it with just one sprite, and one vehicle, and see what kind of configuration will make it work. If that did not solve, I just saw that on my plugin, although you can change offset, you cannot change anchors, I don't remember why I did that. But maybe, changing the character sprite anchor according to the character's direction could solve your issue.
Or even, if you could provide me the sprite sheet, I could try something here. As I understand, you want the car to fit on that spot when facing up/down, the same way it fits when facing left/right, is that it?