I appreciate the opportunity to clarify some of this stuff.

Here's a logical way to look at it.  Any claim of the form "A > B" can be countered with equal reason by the claim "B > A"; hence, all such claims get cancelled out.  This is singularly not the case for a claim of the form "A = B".  So there is a ground for claiming "A = B".  Alternatively, there's a pragmatic way to look at it.  You are in a dispute with P about the proper course of action.  If you wish to reach rational agreement (as contrasted e.g. with agreement imposed by force), one approach guaranteed not to work is to assume out of hand that your interests are more important than P's.  For cannot P assume, with equal legitimacy, that P's interests are more important than yours?  Down that path there is no chance for rational agreement.

Constructivist, I would agree; contractarian, not so much; definitely not interpersonal or intersubjective.  The basic argument is:  

 (A) if you want to be rational about resolving conflicts of interest, then you must regard everyone's interests as equal. 

The truth of (A) does not depend on what anyone's interests happen in fact to be; in particular, it does not depend on whether they are interested in being rational about conflicts of interest.  So, in that respect, it is not hypothetical.   [To be overly clear, while the "then you ... as equal" clause (apodosis/consequent) does depend on persons' interests, (A) as a whole does not.] 

So also, pace Nagel et al., there is no internalist puissance:  (A) will not compel anyone to be moral who does not wish to be.  Moral truth cannot force the strong to be fair to the weak; but it does expose the rational indefensibility of any such unfairness.  And you have the same situation in e.g. logic and math -- those truths do not prevent people from being willfully illogical or innumerate. 

So, finally, (A) is not fundamentally contractarian:  the legitimacy of "A = B" does not result from an agreement between A and B to that effect (e.g. reflecting a shared presumption that they both would benefit more with that supposition than without).  Rather, the legitimacy of "A = B" is prior to any possible agreement between them:  it pre-determines what counts as a reasonable agreement.