Precise terms for directionality in a writing system
Solution 1:
I've looked into this before, and I don't believe there is a specific standard terminology to describe all features of text directionality.
There are several different qualities involved across known languages. Just considering those which are broadly rectilinear in layout, there is the direction in which characters progress, there is the direction in which lines progress, there is the question of whether characters progress in the same direction on each line (and if not, whether they are mirrored or rotated on alternate lines), and perhaps other qualities that I do not recall offhand. Then you have even more unusual scripts which spiral or proceed circumferentially.
I would suggest that in cases where there is a need to distinguish character directionality from line directionality, you would have to distinguish them exactly like that.
I also stumbled upon a working group that have attempted to wrestle with some of these issues for the purposes of computer encoding of text: https://wiki.tei-c.org/index.php?title=Main_Page