It Ain't Over Until it's Over: Keeping Everyone Present during Mediation

This week, I presided over two hearings where the parties were in a hurry to leave.  In one, the case was settled, but in our collective haste, not one of the parties or their lawyers caught the fact that the short-form settlement agreement expressed an agreement to pay $00.00.  This left the Plaintiff's lawyer concerned enough that the following day he sent an email revoking his client's acceptance of the offer!  Of course, all is well and the Defense lawyer agreed that this was an error, not a con, but it still gave me pause for concern about the quick exit made by everyone.
Then the next day, the Plaintiff accepted a mediator's proposal and then left the hearing to pick up her child before the Defendant accepted or rejected.  He did reject, but when I communicated his counter-offer to her lawyer, she was unreachable and I had no choice but to excuse everyone until Plaintiff's lawyer could discuss the counter-offer with his client.  After everyone left, I was unable to reach any one other than the lawyers.  The hard work and close-to, but not yet completed negotiation virtually fell apart because the process had completely changed once all communication was filtered through lawyers and telephones or worse yet (in my opinion) email.
Just like the children's game of "telephone", something is invariably lost in translation when communication is anything other than face to face.  What's more,  the parties lost out on the valuable momentum that was built up during the mediation.  How do you keep the parties physically present until the case is completely resolved?