Yea we considered this but then the rope hangs down into the counterspace beneath and gets in the way. Or in one case, hangs down and gets caught in the fridge when you close the fridge.

Make the rope half the length of the cabinet door, and instead of hanging it way out at the edge of the door, hang it halfway towards the hinge. The rope will hang slightly higher but it'll fit neatly inside the cabinet when the door is closed.

Unfortunately it's double hinged, so the point you'd need to pull down from to get proper leverage on it is at or near the highest point - hang a rope down there that's of useful length and it's by definition longer than half the length of the cabinet, and doesn't fold neatly in.

Maybe there's a different solution though, I'm not sure