Keeping Your Balance in mediation

Mediators are called upon to be chameleons:  we need to take on the stripes of each of the parties, while steadfastly resisting all urges to lean to one side or another, thereby not only compromising our own neutrality, but perhaps tipping the scales of justice.  This week, I found myself less than neutral when a woman younger than I teared up and complained to me that the muscular sprain that she suffered 3 years ago when she slipped in a store that she was suing, has kept her from working, having intimacy with her husband and basically has ruined her life.  She still wears an orthopedic brace and claimed to have severe and disabling pain throughout the 1/2 day hearing.  Despite the good work that I managed to conduct between the parties as to likely outcome of both liability and damages, Plaintiff refused to accept her attorney's recommendation of a respectable settlement/compromise in the disputed claim.
Be reminded that 1 month ago I suffered a fracture of my foot and chipped two bones in my ankle.  I am still wearing a non-weight bearing boot and still managed to conduct no less than 8 hearings since the accident.  Although I am uncomfortable, I am in no real pain and my bones are healing as they are expected to. Still, it was excruciatingly hard for me to summon up genuine sympathy for the Plaintiff--whose injuries, by comparison to mine, were minor and long ago!
At times like these, I need to remind myself that my perspective can never be substituted for the parties in the dispute.  I am engaged to facilitate the analysis--but in the end, the decisions, the risks, the rewards are all in the hands of the disputants.  In Yoga, there is a position of balance that mimics a tree (See inset).  At times of great conflict, it's useful to have such a position to resort to--a kind of momentary "time out" to re-gain that perspective and re-focus on the dispute at hand.  Mediators sometimes call this technique "going to the balcony"--a visual of taking yourself out of the dispute to re-gain that "birds eye view".  I'm not sure I accomplished that in this hearing, but it's a good reminder that even a person with a broken foot needs, occasionally, to balance on one leg.
What techniques do you engage to keep yourself balanced in the negotiation--or is it okay to lean on one side or the other in these circumstances?