A couple of people in the "comfortable" parts of my town have inflatable pool houses. A double-walled rag inflated to look like a quonset hut covers their entire pool, somewhat similar to some of the carnival caves where they toss the kids in to play in a sea of ping-pong balls.

Most of the carny things have a continuously running blower to keep the structure inflated, but the pool-halls (is there a better name?) don't appear to require constant input. No idea what frequency of "maintenance replenishment" of the air is needed, but if the air gets out the hut would just lay on top of the water until you turned the inflator back on.

At least one has been visible over the ten-foot high privacy fence for at least 8 or 9 years, which suggests that the things are fairly durable. (The 10 foot fence - 2 feet taller than the norm - also suggests they're people who just must have a little more than the neighbors so the pool house might be a little more comfortablene$$ than we "more ordinaries" might want to buy into.)

Depending on your layout, shading out all of the sun might not be necessary. A "shelter belt" of trees (or a fence?) on the east to delay the start of warm-up in the morning might keep the pool from "starting hot" when the noon sun hits and begins the main heating, so that the peak temp wouldn't be quite as warm when you want to go for your dip.

For some unknown reason, shading the late afternoon sun seems to have less effect in our area than blocking the morning sun. That may be different where you are(?).

A partial overhead cover (maybe the shallow third of the pool?) might be easier, and cheaper, to arrange than trying to cover everything, especially if you do find that the shallows get warmer than the deep stuff.

Shade for the parts of the pool that get hottest would probably be most helpful, even if they're shaded only part of the time; but you'd need that temperature distribution survey to tell whether it tells you anything useful for making the plans. If your filter/circulation system is fairly aggressive you might find little in the way of temp differences, but in some pools there are fairly large gradients.

John