Map curves to mesh (all faces of the mesh as one face)

Interesting problem!

Your mesh might require some tweaks (trimming it to where it matters, removing the base of the mold, unless you truly need the whole mesh).

Once trimmed, you could apply something like what @DanielPiker has done here:

Playing with that script gives adequate insight!

I have used that approach in the past when [another modeler had questions related to shoe geometry (find that post here).

Here’s another (similar-but-different) topic.

Back to this:
“Your mesh might require some tweaks”

I was referring to simple ones - If you’re allowed to explore, here’s a quick video you could reference:

Then take it from there with what you were attempting already!