You know a lot more about 3D then I do. You wrote that you were wrapping you label around a cylinder. So that is what I did. I know nothing about how to use extrusions like you do. I have just played a little with Adobe preset meshes like the wine bottle, cylinder and sphere. Its easy to put label on cylinders or wrap the earch around a sphere. That is what I did and I also created an opacity map.
View screen captures in new tabs ans scale to actual size.