Okay, I've had this idea in my head which I haven't done much with yet. The
letters are all based on square "cells" with different shapes oriented in
different directions for each point of articulation:

southwest: labials
west: dentals
northwest: alveolars
north: postalveolars, retroflexes
northeast: palatals
east: velars
southeast: uvulars, pharyngeals
south: glottals

The shapes are arrow-like figures with unambigous forms to indicate
stops/affricates, fricatives, nasals and resonants, with modifications to
mark voicelessness or voicing, aspiration, glottalization, labial release,
double articulation, etc.

The vowels would have the following orientations:

northwest: high front
west: mid-high front
southwest: mid-low front
south: low central
southeast: mid-low back
east: mid-high back
northeast: high back
north: mid and high central including schwa

Different shapes for unrounded, rounded, nasal, voiceless, laryngealized,
fronted, backed, centralized, and others.