I've taken a puzzlehead apart in a similar way:
turned halves of the head slightly off the center,
and the moved a perpendicular half in direction of
the other half. That creates a hole in the center
of the cube. Then I put a piece of hard tube/pipe
of a diameter slightly larger then the screw top,
and easily remove the screw. I used a suitable pen
tip cover that I cut for the tube piece.
I do realize that Eastsheen 2x2x2 is not designed to
be a Do-it-yourself cube. Still, is it true that there
is no way to take it apart without breaking it? I would
like to use it a some mods, but then it needs to be
taken apart.