Good Soldier Schweik, if I understand you right ... "Stower, when you use DADGAD, do you play melody on the bass strings, with the thumb, or do you pick out melody on the treble strings ... melody picking CARTER Thumb, or Piedmont" ... you seem to be inferring an American style of playing, where the basic mind-set is chordal (also your reference to jazz infers that) and so hand positions are based on chord shapes. (Carter picking, as I understand it, is very simple picking based on chord shapes, basically a strummed chord with a moving bass - do correct me if I'm wrong as this is not my style of playing.)

That can sound great, in the right hands, but it's not how I play. I tend to perform traditional English and, to my ears, that style doesn't work for the English tradition. I rarely think chordally at all, but rather tend to have a melody line accompanied by a bass line, usually with passing notes between (and often the less like a 'standard chord' the better) or a melody, bass line and a complete inner counter melody.

It's horses for courses. If I'm playing Mediaeval music on guitar or music that originated with the pipes, drones can work very well, either above or below the melody, because that is what the music requires.   

I have a friend who is a very good jazz guitarist, and he would completely agree with "understand about chords, and that you can have all sorts of permutations", as I do, too, but it's largely not the way I chose to play for the material I play. When I make the odd foray into jazz, then I will play chordally and experiment with different inversions and added 9ths, 11ths etc as jazz is made for that.

One last thing. Some years ago Pierre Bensusan decided he would play everything in DADGAD, as he does to this day. I can't imagine anyone accusing PB of sounding samey!