If we are able to define what chord substitutions do not contain avoid tones (modal, but vertically unstable) or chromatics, we could get a great list of harmonic substitutes surely suitable for vertical use. Let`s call them superimpositions.
Superimpositions also should not provoke arpeggio conflicts with basic chords. For instance, there is no place for 7 and b7 or 5 and #5 together (also check alternate spellings).
Every tone of superimposition whether duplicates arpeggio of basic chord, whether works as colorful and stable modal feature – so called tension (2 or 9th, 4 or 11th, 6 or 13th).
Just to be sure: avoid tones are modal upper structures – 9, 11 and 13th`s, – working only as passing or chromatic notes, because of their harmonic instability.
For instance, upper structures of ionian mode are 2, 4, 6; but only 4th (11th) is harmonically unstable. It`s avoid tone. Upper structures of lydian mode are 2, #4, 6; all of them stable, so there`s no avoid tones in lydian mode at all.
Let us hear and compare 4th and #4th vs maj7 chord. Avoids tend to be immediately resolved, until then we feel kind of anxiety.
Most avoid tones meet one basic criteria: they are by minor second (including interval inversions and octave displacement) above the tones of triad (1, 3 and 5). But not always. Perception of harmonic stability is cultural and quite subjective question, therefore some of avoid tones are just recommendable.
There is my personal list of 28 asymmetric scales / modes (suitable for vertical use), with avoid tones marked grey. It will serve as basis for further construction.