For the chinese umbrella system at least one parachute climbs along the tether of the fixed lifter kite, acting the winch and the generator in the ground station via its own tether.
As you mention the parachute(s) can be replaced with autorotation (here flexible) rotor(s) as shown on the video below. I used a central parachute to space the two wings in order to increase the swept area. The central parachute can also have a central hole allowing it to slide along the tether of the fixed lifter kite.
The rotor can climb along the tether of a fixed lifter kite in a similar way. The use is perhaps easier thank to the stability provided by the rotation. And such a rotor can be lighter than a parachute sweeping the same area.