Thanks for the links @Rodread.
Indeed bridling is a concern.
The sketches of my initial post represent a fixed central round kite: only the blades with their common ring rotate. So the bridle (for flygen system version) and also rope drives (for rope drive system version) are or different lengths, being shorter in front of the bottom kite. That said a parachute kite is not very stable by itself: some anti-drift panels could be implemented as for any ram or SS kite. And an almost round kite usually used as a lifter will have to comprise a long tail, and its angle of attack can be too low for the blades rotating around it. Here we speak about stationary rotors with the goal of delivering continuous power.
On the other hand all my photos and the video represent a rotary kite with a central parachute rotating with the wings, and constant bridle lengths: such a rotor cannot fly by itself without a kite lifter (for me it was tiny 0.2 m² or larger 2 m² lifter kites). Here we speak about rotary kites used in reeling (yo-yo, pumping) mode. The central parachute could be something rotating like the one on the video below, and with additional wings:
