For my purposes, I have to return a texture in the original UV layout. Is there a way to either reverse from a perspective applied projection to the original layout or can I in another way maintain the original UV layout while doing a projection map?
Edit: There was a large amount of confusion over what was going on so I've made a demonstration.
The UV that I end up with must have this same layout as I am exporting to a 3rd party software. I then a projection map of an image which results in the flattened 3d UV layout.
I need to somehow get the same effect (an image is applied to a model) while maintaining the original UV layout. Is there a way I can do this in Blender or with other tools?