Came to say that nothing really beats the bottom-up approach you mention, but there WERE some top-down tools over my career that really helped me too:

- Understanding the circle of fifths (and just doing the exercise of playing a simple melody completely through it)

- Understanding the natural tones scale and its mathematical properties (simpler intervals with low integer fractions -> „nicer“ sounding intervals)

- Understanding Euler‘s Tonnetz for the multidimensional relationship of intervals

These were the backings letting me understand a lot of the rationale behind what happens on the keyboard (by all means, a keyboard based instrument makes it SO much easier to grok theory). Though in the end, if you want to play and compose, 80% is building intuition by just trying to first copy styles and second disassembling the chords and melodies behind.