I didn't know that you could destroy a crystal. Now I am in the final chapter, with all crystals awakened, with the Dark Aurora right there.
I want to get the fake ending before the true one. Is there a way to destroy a crystal, at this point?
This is taken from the answer to the other question you asked on the subject.
"Getting the true ending will put you back on the final chapter with all four crystals not yet awakened so you can then proceed to get the false one later (and this also makes Genome Abilities related to the crystal bosses always obtainable)."
So it looks like you can still get the false ending. But not before finishing your true ending.