Car tie down and transmission in PARK or NEUTRAL?

Yes, tranny in park, e-brake on. Since you're building the trailer, you might look into various ways to keep the car on the trailer. I installed D rings on mine for the tie down straps. There are other methods. I would research what might work best for you. I did not like the over the wheel straps. They seem to loosen more than traditional ratchet straps...just my experience.....Dennis