Need help UV unwrapping image texture for baking

Hi all, I want to bake the lighting of the neon sign but I’m having trouble trying to UV unwrap the image texture in order to bake this. When I unwrap the image texture, the image appears to be stretched and scaled up incorrectly.

Right now I have two main objects. One is just a plane with the “dunkin donuts” image texture applied to it. And the other is the board with the neon tubing.

capture2 (this is the node setup for the plane)

Unwrapping the plane object would cause the scaling and rotation of the image texture to be messed up. Any ideas why?

When I unwrap the plane object without scaling the UVs (scaling the UVs would distort the image), it takes up too much space in the UV editor, leaving no room to add in the UVs of the other object (the neon sign). Can I scale down the UVs of the plane object without affecting the image size ratio?

Capture

Thank you.