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Can suicide be halachically acceptable?

This is a strange fact pattern that I thought of and I will explain my premises as I move through it, but the bottom line is whether a person can use suicide as a halachically acceptable behavior:

A person commits murder during first temple times -- cold blooded, premeditated murder on someone who has no family. Whatever parameters necessary for a beis din sanctioned execution are clearly satisfied in terms of warnings and witnesses etc. But the beis din does not find him guilty because of a technicality.

From what I have learned, we are ok with letting guilty people go (in an effort to be overzealous protecting the innocent) because we have faith that Hashem will execute proper judgment and take care of the criminal. One way which (again, piecing this together with something I recall from many years ago) this happens is that someone "accidentally" kills this criminal acting as an unwitting agent of Hashem.

So let's say that this murderer, feeling incredible guilt and remorse, and knowing that he deserves a death kills himself, since he feels he is acting as that agent to bring about proper justice. Is his suicide (which is simply enacting what, he knows, is the proper outcome -- he is putting into effect that heavenly punishment, not taking the deciding power of life and death away from Hashem, or losing faith in Hashem but trying to reaffirm Hashem's might and rectitude) therefore an acceptable behavior because it is a statement of belief in Hashem's justice or is it still wrong?