Like, M3m3 would be a major chord expressed by a major third followed by a minor third. But in first inversion itd be m3P4, a minor third with a perfect fourth after it. Kind of what the idea is with roman numeral inversions, having I be root, I6 be first inversion (with implied third as middle voice, and the 6th being the top voice interval with bass note), and I64 for second inversion, (6th and 4th intervals from bass). Except this system ive been trying to figure out would show the relationship between each note to their closest note up and down. Ideally itd show all relationships, But I think intervals as a unit make sense trying to categorize chords not only by what notes are being played, but their inversions. Sometimes it feels like this way "harmony" or "notation" would make more sense. Best way I can think of it is a stack of geometry upwards like a totem, or stacked figures using the same center (with their corners touching the same imaginary circle).  Do you have a specific way you visualize/categorize relationships in music
visualize it on the piano keyboard