Musical creativity is a different issue. It is very subjective. Someone starts acting like old milonguero when hearing coda, someone tries to emphasize important moments and skips "extra" ones like Godoy. In any case, dancing to the beat or to the music only, or dancing concrete instrument's part is a very mechanistic approach.
Although, perhaps, there is something, that can help us to be inside the music, inside this "stream". My personal formula is to make the music sound from the body, not only from the speakers, as if you were something like electrical conductor. You are the music, no intermediator. Associations have helped me to find and fix this feeling.
The rhythm, whether it is obvious or not, is a "pulse" that exists inside me. My heart can beat an uneven rhythm or regularly, and I feel it different. If I transfer this sensation from my chest to my feet, it helps me walk quite differently than I usually do.
All this, melody, phrases and verses, is like a wide circle inside which I move like a balloon filled with air. It's like breathing some air in and then breathing it out into the movement. Any melody is like breathing to me. Sometimes I unconsciously breathe together with the singer, though I don't know the words. I breathe in exactly when he does to finish my "singing", to finish my movement.