The workflow would be similar to software development or web design. Edit, then run it through a process to see what you get, and then go beck to edit the original.

Edit the map in your graphics editor, then load into G.Projector, pick Stereographic and set the latitude to +/- 90. Look at the polar aspect maps that result and decide what changes you need to make to correct any problems. Then you have to go back to editing the original map in your graphics editor and make the corrections. Try to make small incremental changes rather than adding a lot of detail at once and then trying to fix it.