Is this what the business end of your lift crank looks like?
If so, a workable (but admittedly less than ideal) solution, at least for the short-term, would also be a
Chevrolet lug/spare tire ratchet:
I'm pretty sure Ford and Dodge trucks with underbody spares use a similar tool. The flat-end of these is used to raise/lower the underbody spare tire. You slide the ratchet onto the hex-portion of the shaft and slide the flat into a tube. The one thing missing vs. the Autohome tool is the outside tube to keep the flat on the nub of the shaft you're turning. Should be easy to find if there are old trucks, junkyards, or tool recyclers in your area.
A somewhat crafty welder could probably also build you an adapter using some rod-stock and a spark-plug socket:
Hammer or grind a flat into a piece of round stock; weld the rod into the center-bore of the socket at the appropriate depth; then drive the socket on the outside hex with a larger socket and your favorite ratchet. (Or weld a handle directly onto the socket body...) A socket-adapter like this would also be small enough that keeping it as a spare wouldn't be as space-inefficient as a complete 2nd handle.