In brief, if you are choosing to come clean, then there is no benefit to only coming half-clean, anymmore than there is benefit to washing only one half of a dinner plate. The veil must be lifted entirely for the truth to be revealed. You have talked the talk, now it is time to walk the walk.
An apology made in earnest is a brave and commendable act. But an apology made in dishonesty or deceit is beneath contempt.
It is now up to you to establish for your readers which type of apology this is.
We'll be watching.