So very very rough and imprecise numbers using this and converting compass directions into decimals using pair of points to take these 2 lunar
http://www.movable-type.co.uk/scripts/latlong-vectors.html
1. Take these 2 lat, lon for the moon
6.6252, 56.5709
5.9802, 86.5686
I can derive using "pair of points" the initial "bearing" of 89.526
So (6.6252, 56.5709) with bearing (89.526)
This used in "Intersection of two great-circle paths" should be enough to derive a great circle using the point and bearing.
Doing the same for MESSIER 78 SECTOR RD-T C3-4 which I used as a ref point for Barnard's loop since it's "behind" the area that's permit locked I get a starting coord and bearing of
(56.4487, -146.4587) bearing 91.3634
So using those 2 coords and bearings I get a "Intersection of two great-circle path" result of
3.0028, 123.8983 and an antipode of -3.0028, -56.1017
Now.. changing that around a bit... using the moons coord and bearing and for point 2 the ruins coords and bearing 0
(-31.7877, -128.9711) bearing 0
I get
-6.549, -128.9711 antipode 6.549, 51.0289
So if my math is right and not too far out of whack considering the small arc used for the numbers this should be the point where the moons path intersects with a great circle from the ruins to the poles
-6.549, -128.9711
So maybe trying to calculate that angle will give you a rough estimate.. especially since the bearing for the moon is sooo close to 90