This individual has already proven he is incapable of rehabilitation. There is no reason to maintain his existance at public cost as he has no chance to rejoin society as a "good citizen".
As to the constitution not prohibiting the use of evidence not found in accordance with a proper search, the document does not use that verbage. The supremes using their office and purpose of interpreting law for constitutionality have already determined it was the "intent" of the framers of the constitution to prohibit the use of "tainted" evidence. There is no reason to prohibit unwarranted or unreasonable searches and siezures if the evidence is going to be allowed it in court anyhow. Fruits of a tainted search are not allowed in court. That is the main incentive to insure police use a proper search.
What constitutes a proper search is open at times to interpretation as a judge has the authority to render a search warrant. Cases involving exigency will allow a warrantless search in limited situations. A permissive search granted by the person responsible for the property to be searched do not require a warrant.
As to what the police can do in this case, they have to follow the rule of law lest they themselves be prosecuted for civil rights violations. Of course there is no recourse for the victim of this predator outside of a courtroom and she has to survive to seek it.
What we would like to see of course is the victim found alive and able to continue her life. She will always be haunted by this experiance if she is alive and competant.
As to the normal feelings of those who see this tragedy, yes they are not pleasant. But then again rape is not pleasant either and cannot be expunged or retracted. The victim will live with it for the rest of her life. Anyone who thinks this is not traumatic and just short of being murdered is living in a fantasy world.