Here is an image of my world map. This is an equirectangular projection of my world. The red grid would be a 250 miles2 grid, but obviously it doesn't measure distances horizontally accurately (except at the equator) due to the distortions of the projection but the vertical lines should remain accurate, I believe.
Iota Globe Net 001 GRID.PNG

What I want to do is create more detailed maps of different (and effectively arbitrary) areas of the map, where political boarders, civilizations, and environments and such are mapped out. I want theses "zoomed-in" maps to be as accurate in terms of distance, shape, and area as possible. I'm looking for suggestions on how I might best go about this.

Say I want to map out this region here:
Crop1.png
Which would look something more like this on a globe:
crop2.png

How might you suggest I do this sort of zoom in and redraw while keeping distances and what not to scale as much as possible?

I have the following at my disposal with varying amounts of skill with each and in no particular order:
Camapign Cartographer 3+
Fractal Terrains 3
GPlates
GProjector
GIMP

I do all my final mapping (short of aesthetic changes) in CC3.

Possibly relevant numbers:
Circumference at equator: 16,000 miles
Radius: 2546.5 (rounded to the nearest tenth)
The planet is for all intents and proposes a proper sphere.