Hi Raul,
My first idea was to use the UV, as I had it in my mind, but it has changed and can’t be used in that way for it. The Surface Deformer would work otherwise in a much faster way to achieve this, assuming I know what you want to do, as I guess I got a simplified version (as I ask for :o)
The first thing that I changed was the interpolation method of the Spline. Linear and adaptive makes no sense. Adaptive introduces new (generated, not “visible”) points to the spline if the angle of the curve reaches a limit. A linear Spline has not that kind of curve. Even projected, it stays linear, and with that, the little amount of points is the only information that can be changed.
I rotated the model so I was able to project from my “view” the given Splines (well I connected them for simplicity). I changed the axis of a copy of the spline, so the object origin was in the middle of the head, and scaled it (for x,y,z, each time differently, so the size would work as rail).
I switched off “Scale - Rail” in the Sweep [NURBS] and got even with a few points of the Spline a nice result. You might improve it with a “higher resolution”.
With the “rail” I like to achieve that the lines on the head lay flat (0.5/5.0) was the setting of your Rectangle. Keep that in mind while you scale the copy of the Spline, that each part of it works like a target.
I have deleted the head out of your model, as I think you work on an larger project and don’t like to have things public right now.
All the best
Sassi