See, your first 2D map does not have geographic features drawn. Add them to this map (say Africa contour), and apply the distortion that you are thinking of to everything at once. The geography would become also modified, and when you put it on the sphere, it would be wrong. Therefore, I believe this idea to have some distortion applied would not work.
You may get by in 2D, by drawing graphics in small 2D maps that have limited area and acceptable distortion. You may cut you 2D map into tiles and for each tile use it's own "best" projection.
From the other hand it is easy to create points on a geodesic circle of given radius on the 2D map. For that you'd need to find a function that calculates lat/long of a point at a given distance and azimuth from another point (search for "direct problem Vincenty"). Once you got that, you can generate bunch of equidistant points at a given distance from the point by changing the azimuth from 0 to 360. Making a polygon out of those points in 2D requires more work when the geodesic circle contains a pole, or intersects left or right boundary of the map. Check out how geodesic circles may look like on a flat map here.