Unfortunately it seems some damage is going to happen, you have to prepare for it.
If you live on the highway as I do, you'll see thousands of car movements via transporters every day, they're not all going to arrive in good condition.
Transporters prefer Falcons, Dunnydoors, Tojo's, 4x's etc, with moderate door lengths (easy to squeeze in) and nice high suspension to drive up and down the humps and ramps.
Give them a low sports coupe and it's going to get damaged
OR
It will get pride of place on top of the prime mover, lifted up there by the forklift.
If I'm moving a vehicle within the state, I now use our local tilt tray operator, a small 1-man operation.
For anything else................lots of insurance I guess.