Yes, generally speed records occur crosswind, the kite moving with the boat. It can be the same for a “classic” boat. However the same kite flying by crosswind figures (rotating or by figure-eight) when the boat is going downwind produces more power (as for any electricity AWES in yo-yo mode), but this is not good for speed records with the same special floats, although correct with a classic boat, the kite rotating acting like a spinnaker. So, as you indicate (if I remember correctly) OKE device with only one kite can also handle all gaits crosswind or downwind.
Crosswind both float and kite (1:34):
Crosswind kite but in probably downwind gait for a catamaran (1:12):
