Spent a good part of the day pondering over this, and.... nothing. Tried all manners of triangles, prisms, tetrahedron, tetrahedron nets, but none of the computed coordinates had any planets. Had one that was close, but error margin still felt a bit too high to consider the result.
The problem is, that in case of prism and pyramid we need height, so I used vector magnitude of V1=(Barnards Loop - Sinuefe) for it, but it is a very long shot. I also tried to tetrahedron and polygon net from it, but again, without knowing how to orientate 3rd point in relation to 2 we have (Barnard and synuefe), there is no way to find coordinates. It is very likely I am overlooking something since my astronomy skills are practically nonexistant, which might be a key to proper orientation of pyramid/tetrahedron.
After doing all of this, I have a strong belief that tetrahedron net might show us the coordinates for 3 other sites. Yes, 3 other, making it 4 total, just by the number of monolith or whatever you call them, pillars that hold ancient artifact, due to tetrahedron net having 4 outer angles (including top). Three triangle formations in ruins, while not aligned perfectly, might be an indication to that too. I also think that monolith at obelisk group A is indicating the planet we are on.