Straighten the series of vertices in UV editor

Question

I've got a bottle modeled and I want to put a Nuka-Cola label on it. I took where I want to put it, marked the seam, and unwrapped it. It looks like this: I want to straighten the UV so that it matches the angle of the Label, is there any way I can do this? I understand it will be a bit distorted, but i'll deal with that afterwards.

Here's my project files (Not using Blend-Exchange because you need the images aswell)

Related: http://blender.stackexchange.com/questions/41132/how-do-i-straighten-uv-maps — Paul Gonet, Oct 21 '16 at 20:35
What about using Mesh -> UV Unwrap -> Cylinder ? (You need to be in front + ortho : 5 + 1 ) — Calvin1602, Oct 21 '16 at 21:12

score 10 · Accepted Answer · edited Apr 13 '17 at 12:57

If you don't want to straighten your UV islands (How do I straighten UV maps?), cause in your case it might be very time consuming you might repeat the steps I've shown in the .gif below. In Edit Mode select all faces (A), press U-->Lightmap Pack-->OK. Now select one of the face to make it active, then again press U-->Follow Active Quads-->OK. Your UV island is straight now. Adjust it using G, R and S to fit the image. If your mapped image is upside down just scale it negative 1 (S,Y,-1).

Straighten the series of vertices in UV editor

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