Displacement modifier with custom height map problem here are 3 spheres. I have a problem with stretch on my sphere number 2. I used a Displacement modifier with an image texture (height map), however I guess that the texture is being projected flat, which causes stretch around the middle section.
Sphere number 1 also has a Displacement modifier but this time with blender's built in Voronoi texture. It seems to me like it's not projected flat, there are no stretches and the result is great. 
How can I use Displacement modifier to get perfectly displaced object while using my own height maps? Is there a way I can avoid this flat projection with displacement modifier?


Sphere number 3 was displaced with material (the same height map as sphere 2), with this node set up. Notice the Box projection is key here as flat projection gives almost identical stretch that appears on sphere number 2.

Sphere number 3 Is what I want to achieve but by using displacement modifier instead of material because later on I want to export displaced mesh out of blender. I know I could bake height map out of material and then use it as displacement map just like in this tutorial: Convert material displacement to a mesh - youtube
However, this seems like too many extra steps and too much time wasted especially if I want to do this often and I'm only using a height map not a procedural material. Thank you for your help, have a nice day. 

Here is the blend file.
Youn need to plug the "UV" output from the texture coordinate node, into the image texture node, instead of the "Object" output. If you are using a default sphere, it should already be UV unwrapped.