The system map displays the moons orbital inclination, and argument of priapsis. The orbital inclination can be used to determine the exact path you need to follow on the planets surface to eventually run into the ruins, the priapsis (the point at which the orbiting body is closest to it's parent) could be significant if it turns out that THAT is where the ruins are placed.
There's obviously a step I am missing to determine it's precise location along the moons orbital path. I doubt it's a massively complicated equation but I am really bad at maths.
Unless I'm completely wrong (what a disclaimer!):
Given identical site designs, with moons that rise/set over very similar angles from the site center, the search path will be a circle that is offset parallel to the moon's orbital inclination. Since the angles for moon rise/set at the site are all known, the distance from the moon's orbital inclination can be calculated, and will likely depend upon the radius the the planet which the moon orbits.
Just working from memory of the photos and being at the site... The circumference of the offset (called a small circle in "circle of a sphere" calculations) can be calculated by a triangulation, based on a scalene triangle with the moon's orbit running along the longest leg, and ruins site placed at the opposite angle. The angles are known, it's the distances that need to be figured.
I have doubts the argument of periapsis will matter, unless I'm way off base.
Right now I am too tired from real life the past few days to dig into the actual calculations, like I did when I thought the UA audio-encoded circle represented a Great Circle. But it's the same idea. Perhaps tonight I'll be up to giving this a try. If I'm astray, please someone do post a correction. Thanks.