Most of the time, I carry my board upside, front to the front, with the fin back. I even leave the mastfoot! I have to admit that I'm lazy and that I don't need to go far.
If I travel further, I will remove the fin (and mastfoot) to reduce drag. I put the board upside down, but still with the nose to the front. My board curve follows roughly the curved flow of air around the car. However, since the nose is larger than the tail, It might be better with the tail first? I'll try it next time.