*I don't think I understood your question. What is the reason use such deformed UV? What is your base mesh? And what is your final shape?
Until someone who undertood better answer your Q ... here is a tip.*

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I guess your mesh is always square, just stretched is some direction. So what about ...  
- Select all faces *Unwrap* > **Reset**.  
- With all selected and one face selected as *Active* (bright one) *Unwrap* > **Follow Active Quad**

[![enter image description here][1]][1]

Like that you can get even distribution again for your texture.

[![enter image description here][2]][2]

Also it is still square when view from top, so you can go to *Top View* (7) and *Unwrap* > **From View**

  [1]: https://i.sstatic.net/TiCn6.png
  [2]: https://i.sstatic.net/GZHqz.png