I hauled cars for 3 years using straps on the frame until a guy in Tulsa showed me I was crushing brake lines
I was moving a 2016 Camry from Oklahoma City to Dallas last Tuesday and the owner pointed at a small kink in the brake line behind the rear wheel. I had been looping my tie down straps over the frame rail for 3 years, probably 400 cars, and never once checked what was underneath. He said he used to work at a dealership and saw bent lines all the time from guys like me. I crawled under and saw the line was pressed almost flat against the frame, maybe a quarter inch of clearance gone. Took me 20 minutes with a flashlight to check every car I had on that load and two of them had the same problem starting. Now I run the strap through the wheel and never touch the frame at all. How do you guys strap down a car that has no good frame holes without wrecking something?
Read a post on a tow forum about a guy who uses axle straps with soft loops around the control arm instead of the frame. He said it keeps the strap off the brake and fuel lines and the loops won't cut into anything. Another trick I heard was running the strap through the wheel and crossing it to the other side, which keeps the car from sliding sideways. You can also buy those nylon sleeve protectors to slide over the strap where it touches metal. Just make sure whatever you wrap around can take the pull without bending. Sounds like you already learned the hard way, but checking with a light before you crank down takes two minutes and saves a lot of grief.