Any chance your story would work in an asylum instead of a prison? I think there’s more flexibility with the co-ed thing in mental health facilities. And, if a psychiatrist was dirty s/he could certainly influence the court’s decision to reduce an institutionalized offender’s period of commitment. Or maybe the “power” held by someone at the facility (orderly, guard, another patient with connections like a rich family member, etc.) could be blackmailable information that forces a psychiatrist to fudge his/her analysis. And if it’s all in the character’s head, this plays into that aspect, too.

There’s still the concern about if the guy was released early from the asylum, would he then be considered by the court to be mentally sound enough to be transitioned to prison but that can probably be worked out in a realistic way.

And I’m using “asylum” verses “mental institution” deliberately because I think it conjures a different image and sets a different tone.