There are a few threads out there that discuss the topic of towing with the interior removed. You will find the folks that insist that the interior components, especially the interior skins, provided critical support to the shell. Then, there are others, like myself, who have actually towed their trailers with absolutely no interior, even the interior skins, and have had no issues.
Here is a recent thread:
My summary advice, is that as long as you still have the shell firmly attached to the frame, you should have no fears.
And definitely lift your shell from above. Have a look at the following thread:
Post 9 and 11 show some good pics of what can be done with the gantry frames--you should be able to the same with the crane you speak of. There is also a diagram for building the frames in a pdf at the end.