Dynamically stretch selection to evenly fit rectangular area

[literaldehyde]

Hi, 

 

I'm trying to make a map template for Civ V where I stretch an arbitrary region into a rectangular shape so I can later superimpose a fixed grid over it. 

 

For example in this image I'd like to stretch this selected region over into the rectangular shape in a way that still makes the continents look natural but rescaled:

 

Are there any plugins that can do this? I tried Grid Warp and DistortThis but both were way too tedious as well as not using information from the center of the image to evenly stretch the entire image out. Would you need some kind of unique algorithm to do this? 

 

Alternatively for this image I think I could approximate it by mirroring/stretching the shaded region over the line, but I don't know if this is the optimal way. 

 

Any tips or plugin suggestions?

 

 

Edited December 6, 2018 by literaldehyde
more info