My Eucalyptus Tree

They do that Woo, grow very fast but dont put down enough anchor roots.
My thoughts would be reduce the height drastically and hope it re shoots from the old wood.
I dont think with one of that size you will get it to stay upright once its moved, the trick is to cut back when young so as to stop the top growth outstripping the roots.

 

I'm only guessing really Woo, but it looks quite big, and we are likely to get a few more storms before the winter is out.
Personally I'd cut it down to about 8 to 10 ft, so as to take the leverage out when the wind blows.
If it recovers you will soon be cutting it back again.

 

The wood is pretty soft woo, cuts easily with a bow saw.