NavList:

Tony

As you say the ‘Hinks’ method, of plotting celestial, used by Amundsen, but not by Scott, only works very close to the pole.  When long distance polar flight started to be developed towards the end of WW2, the Greenwich Grid was introduced, which is a square grid based around the Greenwich Meridian.  It is essentially an overlay designed to overcome the problem of dealing with the extreme convergence of the meridians at high latitudes.  It is not a separate form of projection.  It is a steering aid; fixing including CN fixing can often be accomplished using the normal methods.  You can overlay the grid onto any suitable projection, notably the transverse Mercator or the polar stereographic in Polar Regions and the Lamberts conformal in sub-polar regions.  The difference between true direction and grid direction gradually changes as you cross the meridians depending upon the chart projection in use. 

Don’t be frightened of the gyro-compass bit.  Until recently, the main source of directional information in an aircraft was a magnetically monitored gyro compass.  However, close to the poles magnetic monitoring is poor, so you run the compass in a direct gyro mode.  Eventually, the gyro will drift off, so you have to keep checking and correcting it.  A prime method of doing this is using celestial heading checks.  You can do this with an astro compass or a periscopic sextant.  As far as I remember, you calculated the desired body’s true azimuth using AP3270/Ho 249 Volumes one and three, which go up to 89 degrees then apply the current DR difference between true and grid heading to get grid heading. 

So the answer to your question “What do I do at 70 or 80 degrees?” is plot your fixes normally.  As far as I know, that’s what Henry Bowers did all the way to the South Pole.  However, if you still want to learn about ‘grid navigation’, I was going to suggest you could try looking at https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/FAA-H-8083-18.pdf Chapter 14 (N.B. the title to Fig 14-5 is obviously a typo) although they do seem to make rather a meal of it.  However, I now see your link page copies great chunks out of that including the typo under Fig 14.5.
 
For the introduction of the Greenwich Grid, you might try looking up the history of the RAF Aeries Flights,  https://www.rafmuseum.org.uk/documents/Research/RAF-Historical-Society-Journals/Journal-17A-Air-Navigationin-the-RAF.pdf  pages 73-91.  Incidentally, upon P91, there’s a very fine photograph of Dickie Richardson author of the 1941 ‘Alice in Wonderland’ edition of AP1234. DaveP