When the whānau asked for an apology and compensation, Waikato DHB interim chief executive Derek Wright and Webb said the DHB's insurers had complained to the Solicitor-General about "procedural concerns" during the June 2018 inquest by Bain.
Since then Wright has resigned and Webb left after the DHB board was sacked by Health Minister Dr David Clark in May.
Commissioner Karen Poutasi has agreed the DHB will participate in mediation with Macpherson, Stevens and their son Tony Stevens.
Poutasi has met the family twice over the past two months, and agreed to enter mediation talks to be conducted by an independent mediator in Hamilton on July 25.
Jane Stevens said: "We are pleased that the new commissioner has agreed to our request for mediation
"The appalling decision by the previous DHB leadership to try and overturn the Coroner's findings extended and worsened the hurt our family has gone through.
"We hope that we might be near the end of this awful legal journey, and be able to start looking to the future."
Stevens said the family is seeking a "full an unequivocal apology" for the DHB's part in Nicky's death, based on the Coroner's findings; an agreed and appropriate means of remembering Nicky's life as well as costs imposed on the family.