I think this analysis can be as complex as you’d like and still not good enough.
You are on to something but the devil here is in the details; how long tether can you have, how is the rotor oriented, bridling, mass per kite, L/D, everything plays an important part.
In simulations I generally find cosine losses far exceed wing gradient gains. So you end up with the lowest practically useful elevation angle determined by distance to ground and looping radius. Which again may tie in to wingspan and tether length. Tether length again ties in to the L/D of your blades/kites and the solidity of your turbine.
I did make a simulator for this covering «The Pyramid». I dont remember if gradient wind is in there at the moment but I think maybe. The problem in this case is just, «The Pyramid» does not really support very long tethers. Though I’m sure maybe the simulator could be used to produce interesting results for whatever design you are thinking about, if it features rotary power transfer. It would be comparable of course, only a desicated simulation would bring you anywhere close to a precise answer.
Please let me know if you are interested in this, we could run some simulations together.
edit: wind gradient is not there but I am willing to ad it on request. I dont really interest much in wind gradient lately due to the arguments presented above