
Daniel V. answered 05/26/19
Music Theory, Ear Training, Jazz, Saxophone.
Good question, very long and well constructed. My answer will be shorter. I think you partially answered your own question in your list of 3 ideas, but I would add that it's important to think intervallically as well as solfege, especially in music that modulates alot or is just simply nontonal. When there is a clear modulation it is highly recommended to switch to the new "do", and if it is a tonal piece to understand it's relation to the global tonic. The problem you may be facing is in music that is tonal but nonfunctional. For example "Giant Steps" by John Coltrane, the chord changes are BM7-D7-GM7-Bb7-EbM7-Am7-D7- GM7.... All of these chords are normal chords that could be found in Bach, but it's the order (or syntax) that makes it sound nonfunctional. Arguably this piece is in Eb major, and if you were think of it in roman numerals bVI-V/III-III-V-I-(ii-V)/III-III......it's a bit too complicated for people's liking, as it practically modulates every bar to one of 3 keys (I, III, or bVI notice the major third cyclic relationship). As a jazz musician and improviser it's better to think of this progression intervallically. Short answer is that it depends on the music you're playing, but it's always good ear training to think both intervallically on in terms of solfege.