Bargaining with the Mediator

     After over a decade of mediation, I sometimes find that after the information has been exchanged and the negotiation is ready to begin with dollars, the parties are stubbornly resistant to discussing numbers that will land them within the likely "trading zone".  In these instances, I find it is sometimes effective for the mediator to propose her own "hypothetical brackets" to break the impasse before it finds it's way from lines in the sand to footprints in concrete.  By making the bracket "hypothetical", the mediator can take the credit or blame for such outlandish values or suggestions and can also narrow the gap and keep the parties moving. 
     For example, where a party has made an initial pre-mediation demand of $1 million to settle a real estate dispute and the other side could not possibly pay that, even if it agreed, but could, if necessary, satisfy a judgment in the "low 6 figures", the mediator may propose an initial bracket of $100,000 to $500,000 to settle (instead of attempting to negotiate between $1 million and a $10,000. offer all day).  The Plaintiff may not agree, but could then "negotiate with the mediator" to propose a bracket of $250,000 to $750,000, instead of sticking at $1 million or $990,000 in response.  The other side, hoping to end up between $100,000-$300,000 would be resistant to that, but might propose to the mediator that they would accept a bracket of $150,000 to $350,000.  This is a classic "negotiation with the mediator" in the execution of the "what if" game.  The likely starting place for entering into the trading zone would then become $200,000 to $550,000, which may jump start the negotiation considerably from the $990,000 to $10,000 starting place.
     By negotiating with the mediator instead of the opposing party, the disputants are able to test the values and get into the trading zone in a hypothetical way without making offers that become floors or ceilings for further negotiation if it becomes apparent that the parties cannot get into the same "trading zone" on the day of mediation.  Do any other mediators or lawyers find this effective as a strategy to save face and gain information?  Are there ethical considerations that I may be missing here?