If I understand you correctly

, the result should be something like this ...

I guess you have to optimize the UV map.
Bake at this optimized UV map, the texture. This texture store. (for example, texture_testbox.png)
Then you will delete all the materials (in object mode) (save possibly earlier). Then create a new material, with the stored texture (texture_testbox.png). (UV-setting at Coorordinates).
Then export only (object mode), done.