Hey Mike,
Welcome to the forum.
The guys you mentioned would all be great sources for this kind of technical info, I'd listen to them!
My thoughts? Everybody's hands are different, some have long thin fingers, some short and stubby (and some play with a pick). It all comes down to whatever works for you, whatever allows you to get the sound you want or even reach the notes you want to get to.
Unless I run into some crazy written line that forces me to think about my right hand I seldom know what it's doing... But since you asked, let me try to describe what I think is happening - for what it's worth. I wouldn't go so far as to teach this as a legit method - it's just what happened to develop for me.
I think my thing stems from trying to keep everything quiet. When the bass is on and I am not playing, my thumb is resting between the B and E-strings (muting both), my index finger is on the A, middle finger on the D and ring finger on the G. From there, if I want to play a C on the A-string followed quickly by a C on the G-string, or even sound them together, I will use my index finger and my ring finger.
And that's about as organized as it gets... HA! Once I need to play other things my thumb kind of floats around, sometimes resting on the B or even floating above it when I'm playing low notes. Like I said, it's unclear to me what is actually going on down there!
You are right that each finger sounds slightly different but I've never purposely incorporated that (except for the occasional big soft low note plucked with my big soft thumb). I will say that if asked to play straight eighth-notes I try to play them all with one finger instead of alternating - always sounds more even to me... It's my understanding that James Jamerson did all that great playing with only his index finger.
So there you go, whatever works for you is the way to do it!
Cheers,
Jimmy J