XZIIORIOIACKHHGRQX = SIX-SQUARECIPHER--
Using the same way you figured out to solve the 4 squares, where you switched the "X" in the coordinates of each original letter of the pair (digraphic), but as you stated, it can't be just "switched" in a tridimensional coordinate system (x,y,z), so they must be "rotated", taking the ...
I didn't use programming but used a calculator. I think the answer is
First I observed that
So I started searching for
After finding this answer, I decided to check if there are other possible answers (of course using a program).
Turns out there are two more:
The program used:
I still like my original answer the most, because
I believe the solution is the following
What gives me confidence in this one is that it appears carefully crafted to only admit a single line of play.
Replay scroll down to second game. Thanks @Rewan for help with the FEN.