Indeed the lift is not used to sweep the wind area. So I confirm it is a drag-based AWES.
However parachutes can also generate lift, " just to help keep the system elevated". I don’t see any fundamental difference with airfoils in Laddermill configuration.
You promise something for a hypothetical future that you keep decrying in others.
For what I remember a crosswind version has been studied by Wubbo Ockels, named Spidermill. But all this is only a hypothesis, no more.