I have only brought one Corvette over in a container before and I have to say, apart from delays, I had no issues with that process.
I drove it to the port in the US and collected in the UK.
One problem I did have was an incredible attempted bit of deceit by the company doing the SVA.
Once the work was completed, I was oddly asked to pick the car up at night from a private address but even in the dark, I could see the car looked like it had been rally crossed, never seen a car more dirty!
My neighbour at the time, a policeman who had a side valet business set about cleaning it the next morning and was shocked to find a huge scuff on the rear of the car and also on a wing.
As he had cleaned the car upon its arrival pre SVA he new it was 100% immaculate.
Long story short, the SVA company flatly denied they had caused any damage, so I had to take them to court with the policeman as a witness and with the before and after photos.
Days prior to the case, I got a letter of admission and confirmation they would cover any repairs.
Seemingly someone backed it into a wall and also, the person working on the lights scratched the wing with a belt buckle having not put a cover over the area being worked on and then they even deliberately got it dirty to hide the damage!