There are several ways to hold the string up to the Moon, to connect to points in the sky.
They only look different because the viewpoint is one from outwith the observer's.
If you looked at them from your little man's viewpoint, they would all look the same. I refer you to my point above about it not matter whether the string is held with one end or the other nearer or further to you than the line connecting Moon and Sun.
The alignment is along the plane of the triangle mentioned.
EDIT - additionally, if the yellow orb is the sun, with the Moon to the right of the observer, and the orange are other POSSIBLE sun positions, then there are possible string positions for each, indicated by multiple red dotted lines - but there can only be one at any one time ... neither the sun nor the moon can be in two places at once.
Pick one, and a triangle is formed by sun, moon, and observer. It matters not if the plane of that triangle differs from the plane of another triangle, from a different observation at a different time. For each observation, at a particular time, there is only one triangle. Again, see my explanation(s) above. The observer aligns the string with the plane of the triangle, and from his viewpoint it is superimposed on the line connecting sun and moom.
Because he can ONLY have a viewpoint aligned with the plane of the triangle, looking along the sides to sun, moon, or at points along the side connecting them, he cannot perceive if the string is non-parallel to the side opposite him, but can perceive it to be aligned with the plane and the opposite side.
Further EDIT
The blue triangle is the one I described; the orange lines are the observer's string. It connects two sides, and will always be on the plane of the triangle, although it could be non-parallel to the side opposite the observer. This non-parallelness does not matter. Alignment with the plane of the triangle does.