The back-of-the-envelope analysis for kite-based power is very compelling; enough that I tried my hand at designing a kite-powered system in ~2004. I don't think anyone can really appreciate how challenging the engineering (control systems) are for all-weather kite-flying until they just try to reel-in & reel-out a kite on a relatively calm day. I literally couldn't even write-down the differential equation which describes the inverse control path for the kite, when there's one vector for the kite, and one vector for the tether, under the reel-in load; none-the-less, solve the equation, and then get it to work with a freakin' stepper motor.
Don't take the hard maths approach when you can take the lazy AI approach... Just fly a kite by hand, log the data, stick it through a reinforcement learning system to make you a controller that keeps the kite in the air.
Reinforcement learning loves these kind of problems that only have double digit numbers of scalar inputs and outputs.
Either way, my kite flying experience tells me that your reel-motors must move with quite some speed and power if you are to keep the kite in the air when the wind suddenly reverses direction.
I wonder if it would work better if there was a swarm of kites - or at least several deployed in the same area. Far enough from each other to avoid interference, but close enough so they could share data about the air movement.
I agree with the sentiment that going at it from first principles sounds like a nightmare; teaching-by-example AI approach seems like a faster path to success.