OddManOut
Inspired
My idea of the alternate string pickup solves this to some degree because typical voicings would have simple intervals on each pickup. For example a 5th chord (root, 5th, octave) would have the root and octave on one pickup and the 5th on the other. The root and octave intermodulation is all harmonically related, i.e. 100 and 200 gives 100, 200 and 300. The 300 is almost a perfect 12th (octave above a perfect 5th) and there's no subharmonic. The 5th is on it's own pickup so it doesn't contribute any intermodulation.
With a single pickup playing 100, 150, 200 (root, 5, octave) yields 50, 100, 200, 250, 300, 350. Lot more "clutter". And a 5th chord is the least cluttered chord (that's why it's so common in overdriven guitar sounds).
Way back when...maybe sometime in the mid-70's, I had gone to an AES Symposium in NYC and saw the first demonstration of the 360 Systems guitar synth system and was totally blown away. I was a young electrical engineer and was bound and determined to build a guitar synth. Of course I needed a hex pickup so I developed* one using Hall Effect sensors mated to printed circuit boards and 'U' shaped magnets to constrain the magnetic fields to lie along the string and minimize pickup from adjacent strings. Of course there's no need for the Hall Effect sensors, magnet wire will work fine, but if anyone wants to try a '2-channel' pickup, 'U' shaped magnets might help to ensure that each 'channel' picks up predominantly the desired strings and very little of the undesired strings. If you give this a try, let us know how it works out.
* U.S. Pat. No. 4,182,213 Jan 8, 1980. Yup, awarded exactly 41 years ago so the patent is way out of date. Have at it!