The originally intended solution is symmetrical about the diagonal, yep! Though some people have managed to find some asymmetrical solutions as well.
Wow, finally solved it. Actually even though I was only searching for symmetric solutions, the solution I ended up with is not symmetric... ridiculously difficult puzzle.
With that I 100%'d the game, I think. Besides unlocking the locked portion of the outro sequence, are there any other secrets I should be looking for after completing all the bonus X-levels?