Alright. Finally got it working and it's very rough but should get somebody started.
Lunar Orbit and Parallel Orbit for Ruins
Here's, for example, the first site. Indeed the ruins fall right on the line.
http://i.imgur.com/63pCFjY.jpg
To use this download and extract the pages here and open it directly on your desktop
https://www.dropbox.com/s/4k4asdu9lboal9n/lunar-ruin-orbitalpath.zip?dl=0
Gather 2 latitude and longitude readings for a given moon using the following method
In supercruise get the moon as close to the top of the targeting UI as possible and then drop your altitude down below the DRP indicator as seen here.
http://i.imgur.com/mGIwAeT.jpg
This allows you to use your escape vector as a direct overhead pointer to line up with the moon.
Line it up as perfectly as possible and then note the in game date/time and latitude and longitude of your ship.
http://i.imgur.com/ZyLNZ0Q.jpg
Do this twice and enter these coordinates as the Lat/Lon and the radius in km and hit calculate. What you'll get is a visual display of the orbit and the parallel one the ruins should be found on.
A text output with the lunar orbit and the parallel one is also ourput so you can fly from one to another.
Some caveats:
1. Ideally I'd like to host this somewhere. Just don't have anywhere to do so. If you do and would like to please message me.
2. This is very rough. No error catch for inputs, etc. but wanted to put it out there so others could use it to help narrow down their searches.
3. I'm using a map so the orbit can be visualized. Even though the earth is used in the background the proper radius is being used for distance calculations.
4. You have to refresh the page to run a new calculation. I need to add a clear to remove existing markers, etc.
Credits:
I'm using the HTML samples from arc.js
https://github.com/springmeyer/arc.js/
and mostly the calculations and methods from
http://www.movable-type.co.uk/scripts/latlong-vectors.html
I want to thank Suteksio for helping gather coordinates and others for helping to bounce around the math needed to make this work. The library had the tools for it... just had to wrap my head around what had to be done.
As well as Bram Armitage for helping calculate distance ingame so I could verify my tangent and radius calculations
For any questions please message me AdmlAdama on the frontier forums
https://forums.frontier.co.uk/member.php/149570-AdmlAdama