It would appear that saving face is of major concern to all parties (perhaps more so on the part of the Js).  Is it possible that some agreement, at least in theory, had been reached prior to mediation and that both sides, for the sake of saving face are going through mediation for that reason alone? 

Kennedy, in his memoirs, wrote about the seven lessons he learned during the crisis, number six being, "Don't humiliate your opponent," which is, of course, a central face issue.

According to Stella Ting-Toomey, a leading researcher on face theories, face is defined as "the interaction between the degree of threats or considerations one party offers to another party, and the degree of claim for a sense of self-respect (or demand for respect toward one's national image or cultural group) put forth by the other party in a given situation."[2] Specific to face-negotiation theory, face is understood as the image one projects of oneself or one's national image in a public forum. As Brown understood the issue:

Among the most troublesome kinds of problems that arise in negotiation are the intangible issues related to loss of face. In some instances, protecting against loss of face becomes so central an issue that it swamps the importance of the tangible issues at stake and generates intense conflicts that can impede progress toward agreement and increase substantially the costs of conflict resolution

Interesting read

http://www.beyondintractability.org/essay/face/