In the end of each crossing (each reel-out phases) there is a reel-in phase which mitigates the fluctuations due to each U-turn. So the yo-yo mode seems to be suitable for the reversible kite, and all the more so as the reel-in phase occurs at the edge of the flight window, when the kite is slowing down.
A main aspect is that the reversible kite could be quite huge. This aspect emerges from my descriptions (kite span = tether length). As @kitefreak is an (if not the) expert in giant networked kite, as shown with Mothra, I would be glad he plans a realization of a power reversible kite, using elements allowing far higher dimensions than a not networked kite would have. Of course I expect he would use the format he wants to communicate elements of building.