When my car was first being delivered some years ago, the tow ring weld broke loose on one side. The car carriers I have used since then have used 2-inch wide fabric straps around the inner part of the A-arm on both sides at once, with a D-ring in the middle. (I wouldn't let them do it on just one side.) Once on the flatbed, the car is secured using tire harnesses that hold the tires in place and not the body.
The first question I ask when I call is, "Do you have a driver who specializes in antique collector cars." The first time, that got me the owner of the company. Fortunately, I haven't had the need very often, but I now have their card and two drivers' names in my file.