To me it sounds like you’re looking for a way to extend some fundamental concepts of functional harmony while compensating for the use of microtones. Unfortunately, to my knowledge, such a guidebook doesn’t exist. It is likely because microtonality is still not standard practice - it’s use and application typically being pretty specific and situational. However, there is good news, we can puzzle our way through it. Since the application for your purposes is different, in order to figure out chord function on a micro-scale, we have to actually widen the scope of our lenses and look at general chord functions through a very wide lens.
Tension / Release: As others have mentioned, this is a biggie. Triads built diatonically from scale degrees exist on a continuum of tension. However, it’s important to remember that the chords in of themselves do not contain much tension, but it is rather the context through which the chord operates. A major chord in one context may provide a peaceful resolution while that same chord in another context may provide a strong pull somewhere. How are you creating tension / resolution through context? How are you creating that context?
Progression / Regression: In traditionally functional contexts, certain chord relationships result in “progression” or the sense of moving “forward” in a piece while other chord relationships yield a sense of “regression” or the sense of holding back perhaps with a slight feeling of repose. How could you create these same experiences with microtones?
Frequency: No, not talking about individual pitches or Hz, but rather, how often something happens. In traditional harmony, we hear tonic sounds the most, or at least are the most heavily emphasized. In the absence of traditional function, how might you emphasize certain notes over others to establish hierarchy?
Harmonic Pacing: Beyond how often you hear something or how you got there, it also matters when you hear it. In traditional harmony, cadences typically signal the completion of a musical thought, idea, or section. How are you placing your chords to establish function through harmonic pacing? How are you signaling the completion of a musical thought, idea, or section?
In sum, by widening our scope on the role of traditional chords, we’re able to see their application to microtonality. Though by no means comprehensive, this should at least get the ball rolling in terms of creative thinking.
Hope that helps.