UV position problem of Dynamic Texture

Here is the demo showing that it is possible - | Camisa Dimona
More info here How to submit my page to the "made with" section?

As I see your question/problem should be solved in logical way.
Let’s do it in 2D canvas.
We have

  1. Some image to be drawn on canvas

  2. User input (text or image) which should be also drawn at canvas over the first image in some position.

  3. The result = new image on canvas, nothing more
    If you can do it in 2D, there will be no problem to do it in 3D since all these images are actually just flat images (textures). The logic will be the same:

  4. Some image to be drawn on canvas as diffuseTexture. This is flat image.

  5. User input (text or image) which should be also drawn at canvas over the first image in some position. This is also flat image.

  6. The result = new image on canvas, nothing more. This new image = new diffuseTexture which you need just to change after user input.

You can try just to edit your texture in Inspector to see the logo position in 3D and 2D simultaneously: