If you mount a spacer (slightly thicker than the drip edge) in the area between the door and the drip edge, could you then move the camera up so that it clears the door and overhangs the drip edge? Would this achieve what you're looking for? It's tough to judge by looking at the picture, and I don't have a camera at home to look at.
Another option is to mount it on the door. Make sure it's low enough there's no concern with it hitting the ground when the door is opened. Then be sure to route the cable to minimize flex when the door opens. Maybe something like this?
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