Thanks for you reply Quinn!
Indeed, in this score the pitches are completely indeterminate, they are not eighth tones as the accidentals imply, they are approximated to eighth tones for visual purposes only. The only practical way to play this that I can think of would be to create software that automatically mapped pitches onto keyboard keys (of the performers' choice), factoring in surrounding notes that the player has performed (so that the same key can be used for different pitches at different points in the performance) -- so the performer would create their own score with their own (conventional) accidentals for performance purposes. Either that or some huge abomination of a midi instrument that would require tremendous virtuosity.
Custom staves are an interesting point that I hadn't considered, but how could one produce precise pitch notation on a stave with non linear (and non octave-repeating) temperaments?
Indeed, I thought that, for example, indicating seconds was too precise for me, but I suppose there's no reason it has to be that precise as the "sections" of seconds are only relative to one other, which frees up the space to have more metered notes which this score definitely needs. And yes vertical indication definitely needed as the notation software does not readjust the positions of noteheads after you hide stems.