Andy_K :
You could just take the whole lot apart and post the main bits other than the case.
then re-build once it arrives in the US with a new case...
Not sure if it's worth the effort, but you could wrap the components properly and for less money than risk posting the whole machine.
This is what I did when I last moved between continents.
At the time I was a bit of a serial-expat though, so I kept my original boxes knowing I might have to do it. Including the original form-fitted, non-static filling of the box.
Also, my components then spent 3 weeks between ships in Malaysia somewhere . . . . .
Unrelated, I have seen people book seats for PCs. Well . . . seen once and read posts on twitter.