I finished printing the 27 pieces and assembled the top (without the springs):
I used white ABS for the tip and crown, and the rest of the pieces I printed in orange, blue (PETG) and yellow (PLA). Note that each piece, besides the tip and crown, comes as three copies (6 faces + 8 corners + 12 edges = 26 = 2 + 3 x 8 ).
It spun well on the floor. But when I tried to boomerang it, I forgot that with the wide neck of the tip I had to pull harder: it flew away, crashed on the hard floor and 3 pieces (all PETG) broke

. So now I need to reprint them. I guess I also need to get springs, although they don't seem indispensable.
It worked better than I expected as a puzzle, without having to sand the pieces. It seems to me that with my color scheme, the puzzle is completely equivalent to a 3x3 Rubik cube as all the pieces can go in just one place, given their shape and color. So the difficulty to solve it would be the same as that of the original Rubik cube.