Remove annoying texture offset on custom mesh

Hi guys, How can I remove an annoying texture offset on my custom mesh? The offset looks like this (offset on the left side):

It would be great to fix the problem without changing UV, if possible. Clamp wrap mode won't help (the offset still will be there, but lines instead of pic).

I try to reach such result:

Now I can get such result only when I'm changing mainTextureOffset manually, but I want to change it dynamically, relying on the size of the object. The main question is how can I paint the texture from the edge of the object?