My last few experiences with that deal were not good; in one case someone handling the car killed its near-fresh clutch.
Two of them didn't communicate or bother with the scheduled time-frame.
The cars were shuffled, and the "enclosed" was basically a covered wagon the left the cars filthy.
In my case, I'm off the beaten path, so the big and nice carriers don't come near here.

Gotta be a private guy or someone with an enclosed trailer in my area, hopefully the OP is on/near a major route.