But unless you are right on the equator, the moon doesn't go directly overhead, east to west... does it? It doesn't here... makes an arc across the southern sky.
Correct. The vertical angle of the Yagi is set
by the length of the front prop, making a
triangle with the (extended) Yagi length and
the distance between the ground anchors.
If the moon only reaches, say, 45 degrees on
a given pass, then you adjust the length of
the front prop for that, and the antenna won’t
point due East or West at the ends of travel,
but further to the South.
This method may not track the moon exactly,
but with a bit of compromise between the
angles for the center and the ends of the path,
lt may be close enough, depending on the
beamwidth of the antenna.