So I'm now safely able to say I've reached the endgame of BOTW, some several days of real time in. I've done all 120 shrines, maxed out my stats, completed the sword trials. We're pushing forward, and only a few sidequests are left before I go punch Ganon's face in.
@ProblematicUser420's insight stuck with me on the motion puzzles, however, and I'm glad he talked it up. I found it weird he'd have such a different experience with them than I did, and decided: "fuck it, I'm having friends over later this week anyway, let's run a test, because there's something I'm suspicious of."
That suspicion would turn out to be right, but I'm getting ahead of myself.
So I borrowed one of my friends' corded switch Controllers (the one he uses for Smash), fired up an earlier save, and tested some of the shrine motion puzzles with it. Surprising exactly no one who suspected it might be the hardware, it was - the corded controller worked perfectly, and was way more responsive than my Pro Controller or JoyCons. There was none of the "Puzzle won't flatten out the way it was before, even when set down on a tabletop" that drove me absolutely buggy.
While I won't say the Switch's controllers have the turnover rate of say, the N64's controllers, both my control methods had issues with the Gyro controls, and that was mostly responsible for having such a miserable time with that goddamn set of trials.