NavList:

Sean C you wrote:  Perhaps one could construct a conformal plotting sheet for high latitudes by using different oblique lines for each parallel and drawing the meridians in as curves. But, I've never tried it and I'm not sure it would be convenient or produce an accurate enough (or even useful) approximation for plotting.

In 1909, the British astronomer Arthur R Hicks https://en.wikipedia.org/wiki/Arthur_Robert_Hinks suggested an extremely simple way of plotting position lines at the poles.  I’ve not been able to obtain copies of that seminar, but I suspect it relied upon assuming P and Z of the PZX triangle as coincident and working with the resultant two dimensional arc.  He returned to this theme in 1944 when he used the method to analyse the Sun shots taken by Amundsen and Scott’s navigator Bowers at the South Pole, The Observations of Amundsen and Scott at the South Pole. The Geographical Journal Vol CIII No 4 April 1944 p 160-180, available here (with conditions) https://www.jstor.org/stable/1789249?seq=1#page_scan_tab_contents  As far as I can see, they were close enough to the Pole for him to use a simple “dartboard” azimuthal projection centred at the Pole.  I don’t know how far away from the pole this system would work, but I don’t think it could extend very far. 

For greater coverage you could work with a Transverse Mercator or a Polar Stereographic chart. If you didn't like the convergence of the meridians, you could work in “grid” (see https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/FAA-H-8083-18.pdf Ch14).  Then your chartlet could be simple graph paper with grid north at the top and your DR or assumed position at the centre.  You’d have to remember to use grid azimuth by adding the difference between grid and true north to tabulated azimuth, and transfer any fix obtained to your main chart using grid coordinates.  Your real lat and long for the computation of Hc would be taken from your main plotting chart.  DaveP