I think communicating with your mediator is the best way to resolve this.
Also, it is important to understand under what context things are said. When someone does not have all the information things can get misinterpreted.
I also do not think it is helpful to publish trader / mediator chats during an ongoing dispute without the consent of all parties.
Remember mediation is about making suggestions not delivering verdicts. If a trader is unhappy with an outcome they have the option of taking the trade to arbitration.
In summary I think it would be better to complete the trade and then, if appropriate, look to do a postmortem / discussion of issue.