I know the pattern doesnt stretch in real life, foil doesnt stretch. But there is literally no other solution. It doesnt matter what you do with the material projection, or UVs, you are asking for the impossible, it cannot be done. The only way it will work is if your 3d model incorporates the same folds, creases and imperfections that you see in the photos.
You have to model the folding of the foil to keep your even pattern, there is physically no way to make it work on a smooth crease-less foil neck.
Go take a look on turbosquid:
https://www.turbosquid.com/Search/Index.cfm?keyword=champagne+bottle&media_typeid=2
Every champagne bottle on there either;
Doesnt have a pattern on the neck
Has the pattern squash and stretch
Has the pattern cut off 4 times with cubic projection with seams
Curls the whole pattern around like a beer bottle neck label
Here, cubic mapping using folded flaps to hide the seams.
even diamonds and cyl shape test.zip