I always have my car in park when it's on the trailer. No problems thus far. I use an over-the-wheel strap on each wheel, anchored at 3 spots per tire into e-track.

DynoDave
Walter P. Chrysler Club - Great Lakes Region
Member # 12304
1970 Plymouth Duster
1972 Dodge Charger Rallye
https://wichargerguy.proboards.com/
1977 Chrysler Cordoba