So am I good to go with breaking the referenced anti-pattern in these specific circumstances?
I think you're good.
I would do (have done) it myself: especially if a Child must always have a Parent, so that assigning it to the Parent is logically part of constructing the Child.
Or is there some consideration that I missed?
One difference is that if the set property throws an exception, then the object is not constructed. That makes a difference if the child is disposable.
using (Child child = new Child())
{
Child.Parent = null; // throws an exception
... etc ...
} // child.Dispose is invoked
versus
using (Child child = new Child(null)) // throws an exception
{
... etc ...
} // child.Dispose is not invoked