What will (or should) SCOTUS do on the Kennedy rehearing petition?

Among lots of good new stuff at StandDown Texas Project is this interesting op-ed from Peter Verniero, who served as a New Jersey Supreme Court justice and state attorney general, on the Kennedy child rape case.  The piece is headlined "To maintain its integrity, the court must own up," and here is how it starts and ends:

There is something almost sacrosanct about recitations of law contained in decisions of the U.S. Supreme Court.  Lower-court judges, attorneys, law professors and everyday citizens depend on those statements in myriad ways even when disagreeing with the court's conclusions. If for no other reason than that, the court should reconsider and correct an opinion it filed at the end of its last term, Kennedy vs. Louisiana....

[H]ow one feels about the death penalty is irrelevant to whether the high court should reconsider its Louisiana decision.  At stake is not a policy debate but the reputation of the judiciary.  If court decisions are to retain legitimacy in a free society, they must be based on accurate readings of the law. From that perspective, unless or until it is corrected, the Louisiana opinion will suffer under a cloud of doubt....  Whether the court ultimately reverses its decision will depend on the court's evaluation of a correct survey of the law. Until that happens, we will be left wondering whether its divided Louisiana ruling is entitled to respect based on an accurate review of the law or merely because the court decreed it to be so.

It is unclear whether the author of this op-ed would be content if the Justices just amend the Kennedy opinion by adding a footnote discussing the (lack of) impact of military law on the analysis.  I suspect that the adding of such a footnote through an amended opinion is all that the Supreme Court will ultimately do in response to Louisiana's rehearing position.  And perhaps this is all the Court should do, since the flaw of the decision does not rest in its failure to discuss military child rape law, but rather in five Justices' clear desire to use constitutional doctrine to block any expansion of the death penalty in American states. 

In short, as I have explained in prior posts noted below, I consider the Kennedy decision to be misguided as a matter of constitutional law and policy.  But, unless someone in the Kennedy majority is prepared to reconsider more fundamental aspect of this recent ruling, I doubt that the military law kerfuffle should (or will) change the outcome.

So, dear readers, after I have here reiterated my Kennedy views and predictions, what do you think SCOTUS will (or should) do in response to Louisiana's rehearing position?

Some related posts the Kennedy ruling and a possible rehearing:

• Could all the mistakes in Kennedy be corrected?
• Louisiana seeks rehearing in Kennedy child rape case (with some notable lawyers helping out)
• Additional briefing in Kennedy child rape rehearing debate
• Will the Supreme Court rehear Kennedy v. Louisiana?
• Washington Post editorial supports rehearing in Kennedy child rape case
• The international dogs that did not bark in Kennedy
• Ineffective assistance (by prosecutors) in Kennedy child rape case?
• Some first-cut reactions to Justice Kennedy's work in Kennedy
• Culture of life trumps democracy and state experimentation in Kennedy
• Will (and can) "outraged" politicians really do anything about Kennedy?
• Counting to five in the Kennedy rehearing debate
• Add Prof. Tribe to those urging rehearing in Kennedy
• Deep thoughts about Kennedy while rehearing motion pending