The model probably has loads of unnecessary geometry in it, but as an initial thing, try to “purge” the model (Window | Model Info | Statistics | Purge unused) and see if it reduces.
If you have the image as a flat label (jpg image file), then the texture will wrap around any curve, but you need to turn hidden geometry on and paint each facet as it turns the corner:
The problem is that the surface you are trying to paint on is not vertical, so the corner tapers as it turns - a flat bit of paper would crease and wrinkle, so a flat texture will only map the image where the paper would touch the surface. By filling each surface with the texture you have the ability to select exactly which bit of the paper (texture) touches: r-click and position texture… If you had the patience you could even distort each instance by a fraction so that you stretch the image to fit rather than wrinkle it.
(Note that the pipette tool will lift a texture’s position/distortion so that the paint tool will replicate it)