How to calculate UVs for a mesh created in runtime based on Vertex position

So I'm creating a 3d first person shooter game based on an older 2d game called Liero. The central element to the game is that both players are underground, and must blast their way through dirt to reach each other.

I've achieved this effect through the use of voxels, but I'm stumped as to how to shade them. I've looked up a lot of different techniques for mapping uvs, such as Tri-planar, but either I haven't understood them or they haven't worked (maybe both).

Currently in my implementation I calculate out the vertices for my mesh and then assign some UV value to that vertice which sticks with it. Note that I don't neccesarily have 3 vertices per triangle, as multiple triangles may share a single vertice (and be facing different directions).

I don't need it to be super precise, and in fact I like the somewhat random look I get when the UVs aren't super precise. However, as can be seen in the screen shot, when I have certain angles I get a sort of stretched look which is very unnatural looking. I believe this is caused by the UVs of two vertices being identical or near identical. So my question is really thus. Is there some good way of converting 3d vertices into 2d uvs in a way that doesn't produce adjacent symmetries or stretch out the UV unnaturally?

Currently my code for calculating the UV (as seen in the picture) is:

  private Vector2 calculateUV(Vector3 position)
     {
         float greatest;
         float middle;
         float smallest;
         position = new Vector3 ((position.x)*15f/17f+ voxelRadius/7f*5f, (position.y)*13f/17f + voxelRadius/7f*3f, (position.z)*11f/17f + voxelRadius/7f);
         if (position.x > position.y) {
             if (position.x > position.z) {
                 greatest = position.x;
                 if (position.y > position.z) {
                     middle = position.y;
                     smallest = position.z;
                 } else {
                     middle = position.z;
                     smallest = position.y;
                 }
             } else {
                 greatest = position.z;
                 middle = position.x;
                 smallest = position.y;
             }
         } else if (position.x > position.z) {
             greatest = position.y;
             middle = position.x;
             smallest = position.z;
         } else {
             if (position.y > position.z) {
                 greatest = position.y;
                 middle = position.z;
                 smallest = position.x;
             } else {
                 greatest = position.z;
                 middle = position.y;
                 smallest = position.x;
             }
         }
         return new Vector2 (greatest/25+smallest/25, middle/25+smallest/25);
     }

Yes, the code is pretty random, and was made up on the fly in order to try and remove as much stretching as possible (and it has some) Thanks in advance!!

[1]: /storage/temp/78055-dirt.png