What is the best way to display a polar region on a world map?

[Koleeflour]

Hi there, sorry i haven't posted in a couple of years. I've still been keeping up with map making and worldbuilding, but normally whenever i have a query i found that somebody has already asked the same thing on this site and been given an answer that helps me out. I'm a bit stuck here though.

Iv'e been designing this world for some time now. Iv'e been paying close attention to plate tectonics when making this map, as i wanted it to have a sense of realism. I came up with this.


Note: The northern region of the map looks very large and distorted. This is due to the map projection. The northern region actually looks like this.


The northern region is incredibly important both politically and culturally. There is a city on the north pole which the people of this world value as a centre of religion and philosophy (similar to Earth's Vatican city). With it being such an important area, it didn't feel right going with an equirectangular map, relegating the north pole to a small boxed out section in the corner. Even if that were the case, the northern region just looks ugly and too distorted plotted in any cylindrical projection. Not to mention the people of this world are not human. Cylindrical projections may not necessarily be the norm for them. It is probably important to note also, that this world is quite a lot hotter than Earth, and that there are no polar ice caps.

What I'm looking for here is any advise or suggestions in regards to this problem. Any help would be most appreciated.