I love how you use variations of a puzzle to mod into other 3x3 variations.
One idea I have is to transform the Curvy Copter into a tetrahedron?
Maybe that's a little crazy.
There's a problem with the build up. A 3x3x3 can be built up into any size, because all cuts have intersected inside the solid and than stay parallel as they intersect with the cube's surface.
On a helicopter cube, the cuts meet exactly at the surface. Building up any material will result in the need of additional (floating/groove mechanism as a straightforeward aproach) parts. The first ones you need are those found on TomZ' Curvy Copter II and the helicopter octahedron.
If you want a Tetrahedron that's only a shape transformation you would have to cut the cube down that far. I don't think it would still be intact. Maybe the "cheat" also done here is possible: http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1632
I never found that really cool though.