Doesn’t seem to be any easy way to unfold the cone and take the curves with it.
But if you cut the solid you can then flatten.
I cannot save the model in Eval mode on this PC but here is the outcome.
The pattern.
I just thickened the curves during extrude as bodies. There is a limit to how thin that need to be.
Pattern Subtract.
Does that help at all.
Cheers - Paul