Uhhhhh I would move things far enough out of the way so you don't hit the door. My garage ceiling is only about 8-9 feet and this is why I pull things out the top. However you could attach to the front bumper and with a short chain.. I'd assume the roof/hood would be higher than the picker at that point.

Problem I see is you have to put your subframe onto blocks or something to keep it from resting on the engine hoist legs if you have one that goes under the car like most.