OK, I've done some more work and my major problem boils down to this:
Given the two extension lines that form the angular dimension, and the
location of the dimension arc, how can one distinguish between the cases of
actual >180 deg angle dimensioning (as in the case of a circle), and the 4
acute subcases of angular dimensioning (as in the case of two lines). In
the latter case, ACAD does not allow angles >180 deg, and reflects the
extension line(s) as necessary to produce this result. In the case of
angular dimensions of circles, all angles are permitted. Without knowing
which pair of extension points represent the CW line and which the CCW
line, I'm having difficulty distinguishing the cases. I can swap the
extension lines if I don't detect the dimension arc between them (in the
correct order) but this method produces incorrect angular dimension in the
case of lines half the time. I must be missing something obvious. Go
ahead, make me feel foolish, please.