Mediation?
You can't negotiate yourself out of a shitty situation. Harsh, but, true.
The focus has to be 1.wellbeing of the child, 2.hand holding of the parents.
Grief is mediated by knowing that everything possible was done, and was done well. If you don't believe that was done, well, that must be agonising. I'm desperately sorry for these parents, and, I'm very glad I have no idea about how they feel, but, FFS.
Mediation happens every day, all day in hospitals, they do it well because, sadly, this is bread and butter work. This was a wildly different set of circumstances that exasperated every single intervention, treatment, flowchart, protocol and bit of common sense.
I'd be very surprised if there was a benefit to this going through the courts.