Surface Morph - W with constant direction

Hello everybody,

I need to morph a "2D" complexe texture on a "2.5D" multi-curved surface, I have been using Surface morph so far. It works great for mapping the texture in U and V direction.

But I am not happy with the W direction (logically following the normal of the surface).
Here I'd the texture (geometry input) to be morph in U and V direction, but keeping its initial and constant W direction. See the screenshot about the ideal "morph box" where W follows Z direction.

I am not sure if this is complete non-sense or feasible.

Please, do not pay attention to the texture design, it is a basic design used as exemple. Ideally, I would avoid to change the texture construction. Here, I am purely asking if this kind of box morphing is possible or not.

Thank you very much.

L