So if you repeat that with all 12 edges you'll get surfaces like the attached.

It still needs some problematic bunching and slivery intersections to resolve but it's 12 surfaces to work with instead of a whole lot of arrayed solids so probably better.

If some extra space is ok maybe something like arraying a cutting plane along the path and intersecting those with the 12 surfaces could yield some cross sections.

- MIchael

Great suggestions! With the first example, I failed to trim about 10% of the surfaces.
I finally succeeded with a simpler case: the source solid is a tetrahedron, and the path curvature is smoother.
The trim tool ultimately worked better than the boolean merge, so I might go back and try that on the first example.

the resulting solid:


overlayed with arrray:


the tetrahedron "engraving" into a substrate: