I sometimes think we all get caught up in being able to pin a name on something and we get lost on what is trying to be said.
Putting a name on something means different things to many people.
From what I gather the OP would like a fuller fatter tone as he goes above the staff.
But there again Im putting a NAME on something.
For me there is a:
Thin sound up top
Brittle sound up top
Fat sound up top
Then you get into PROJECTION which becomes a whole new subject.