Mathematical side of music theory

My reasoning goes like this: if a chord can be ended on in a cadence, then it is made up of just minor and major thirds. Both major and minor tonic, subdominant, dominant, and submediant able to do this. By necessity, the mediant is also made up of just thirds (E to G and G to B are in tonic and dominant). 

(all that proceed form here will be in terms of natural major and minor degrees)

Now, I look at leading tones. the VII in major and the raised VII  in minor lead to I, The lowered VI in major and the natural VI in minor lead to V, the natural IV in major leads to III, and the natural II in minor leads to III. They all have a consistent just minor second ratio (15 to 16) to their respective stable degree. From this observation, It seems all leading tones have this property, allowing chromaticism for our next part.

The chromatic leading tones are as such: lowered II( (leads to I), raised II (leads to major III), lowered IV (leads to minor III), and raised IV (leads to V). 

By plotting the degrees according to interval, (degrees by a just perfect fifth are horizontal to each other and placing the third of the major chord above the middle and the third of he minor chord below) we get this chart, which is very similar to the Neo-Riemannian theory graph as it is based off of similar principles. 

I use this instead as a tuning principle (secondary functions complicates this) without enharmonic equivalents. Due to this, the interval between II and IV is not a just minor third. 

This creates problems as secondary functions to chords with non-just intervals in tuning. How would one solve this?