wordn’t

there should be a subtle difference between the two signals

Not really. It sounds generally like you’re overvaluing the role of a plane relative to the magnetic poles. The string moves somewhat circularly, like a jump rope. It doesn’t matter how you angularly orient the pickups, all else being equal.

As for per-string pickips, hey, I’m all for it. Give me 6 output jacks as well so that each string can get its own effects chain.

Have you ever considered getting into synthesizers? Based on your thoughts I feel like you’d really enjoy making synth patches

a guitar pickup appears to be more of a two dimensional sensor that picks up the motion of a ferromagnetic string in the two primary directions of motion

It’s actually not a 2 dimensional sensor. It’s 1D, the velocity of the string induces a current in the coil (Faraday’s law)

there are more complex harmonic motions present than a pickup can register in two dimensions

Again not sure where 2d is coming from, but the current perfectly corresponds to the velocity of the string, which we already know is identical to the sum of the velocities created by all of the harmonics (Fourier Transformation).

How did you reach the conclusion that some harmonics are missing from the resultant signal?

the coil and slugs of a pickup are surrounded by a single large winding, yet the strings each have very different frequencies

The human ear also has different sensitivity to amplitudes at different frequencies, with higher pitched sounds not needing as much energy to reach the pain threshold. The distance between each string and the pickups is also adjusted during setups, sometimes including tilting the pickups themselves depending on the type of guitar.

Just a few thoughts I had while reading. This style of pickup really is just popular just because the’ve been popular for so long and they’re supremely reliable even with as much abuse as we put guitars through. There are others; you might enjoy reading about the physics of a piezo pickup, and the problems they often create for players haha