Originalism and the "Good Faith Exception" to the 4th Amendment

Over at Patterico's place, they've been discussing Alito's dissent in Doe v. Groody. Commenter biwah posed a challenge to "all the textualists/originalists":

Question for all the textualists/originalists, where is the Good-Faith (aka “oops”) exception in the Fourth Amendment? Is it “built in” to the reasonableness requirement? That seems to be the only hint of potential legitimacy of the Oops exception. But then, where else is accident an excuse for an acknowledged violation of the Bill of Rights? Is there any textual/original support for such a perverse proposition? I don’t think so.

My response is here