Dynamic Paint + Shrink-wrap

I am animating a paper roll “sticking” on to a surface (kind of “u” shape).
Thanks to a user from the forum @skuax I managed to learn a lot in this particular matter of animating an unrolling surface. I am actually using one of his tips using dynamic paint to simulate how the paper roll gets glued to a surface.
Basically I have a surface with a curve modifier (following a spiral curve) and while the curve gets animated in one direction the surface unfolds. Then there is a mesh working as a “dynamic brush” and while the roll moves in one direction (unfolding) the brush follows the surface (scale in one axis) and the surface progressively shrink wraps on the “mold” (shrink wrap reference shape).
The paper roll also has applied a dynamic paint as a canvas in order to make this simulation possibe,

I manage to make it once…with a “flatter” surface as the shrink wrap reference shape “mold” , but now I would like to perform the same simulation sticking to a different surface ( “u” type shape).

Here some print screens:

And now with the dynamic paint on, meaning the shrinkwrap situation:

You can observe how the surface does not wrap correctly. I understand the solution might demand my file, but unfortunately I can not share it. Maybe someone knows what is happening or what to check by looking at the pictures. I might be able to create a “fake” scene to share it .

Thank you so much

Ok, this sounds stupid, but I think I find a way, not the nicest mesh, but it does what I was expecting.
Apparently there is a inside the shrink wrap modifier there is a “mode” tab. I choose Mode>project Z axis and now the shrink wrap, wraps vertically. It is not the nicest mesh/outcome, but It was the only mode that manage to calculate this.

Still if you have a different approach to wrap the surface without doing it strictly in Z axis and have a gentler wrap I really appreciate it. At least now I can manage to deliver an acceptable outcome.

I think the simple solution is make an invisible mesh for the shrinkwrap target that conforms to the result you want. So it’s not visible (no light bounces) in the render, but is present as a target for the modifiers, unless I’ve misunderstood how you’re doing this.

I am afraid something got lost in translation.
Not sure where, but the concern is about how the mesh wraps onto the shrinkwrap surface.
The surface working as the shrinkwrap shape is invisible already.