Update:
BA have decided this could not be put on a plane (again, TSA are fine with it

) so I now have to arrange shipping.
Does anyone have any suggestions? The problem I'm having is I need something collected from LAX then sent to me in the UK... most places don't want to do this for some reason!
Surely people must have run into something like this before? BAEC in the UK have been great but I still can't get my property back!