Me, Kiwi, and I use a similar method to yours when singing and/or playing. In improvising harmony I use my 50 odd years of intuition and, more recently some music theory, like when to use the third note of the chord, and when to use the fifth. Taking a few lessons in stand up bass taught me how to build walk-ups (and downs).
Our martinet of a choir director taught us all in high school to learn to identify intervals, and while he brought a lot of terror into my life at the time, the gift for hearing an interval and knowing where it falls in the scale has long outlasted the way he treated us.
my experience with him did shift me from classical choral entirely into folk, but it being the sixties had a lot to do with that too.
My mother says I would have been normal if I hadn't gone to college in the sixties.
Blessings,
Barbara