Shrinkwrapping a flat object on a curved object

How do I approach modeling this grill which is curved on the Y-axis and Z-axis? The closest result I got is this, using project,:

The shape I want to achieve is this:

First I thought of using image texture with transparency, but it would not look good because I also need to add thickness and bevel to it.

Done. I rotated the mesh to match the z-axis angle. I also extruded the shrinkwrap base to compensate for the artifacts.

However, not sure if the same technique can be applied for more complex objects like this:

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