Kinetic energy is dependent on mass and velocity squared. We saw that kinetic energy worsened the mass issue, both preventing to maintain speed in the climbing path.
A mean to partially solve both cosine and kinetic energy issues would be using a tower. In the process, you replace the crosswind kite with conventional wind turbine blades.
Or, if one wants to stay within AWE, to capture high-altitude winds, tether-aligned of type parasail AWES, although still underestimated, could be a possibility. This is what the trials mentioned on this topic could lead to, showing that the superiority of the crosswind kite over a parachute kite of the same area is far from overwhelming: one should not confuse peaks of force or power with the average force or power (see below).
This rough estimate made on a small scale could be corroborated by (in French) SkySails — Wikipédia:
La voile peut opérer à une altitude comprise entre 100 et 300 mètres où l’on trouve des vents plus forts et plus stables et délivre 2 à 3 fois plus de puissance au mètre carré qu’une voile conventionnelle.
Translation:
Sailing can operate at an altitude between 100 and 300 meters where stronger and more stable winds can be found, delivering 2 to 3 times more power per square meter than a conventional sail.