One of the controversial aspects of the historian's research, is that she is counting stillbirths among the 800, as "children who died at the home." Normally, however, mortality rates are calculated as a percentage of live births. You can see how including still births would slant the figures above the national average. Still births were very common right up until the 60s, and are often seen even now, with all our advances.
Another issue, not much discussed, is that children born to unmarried teenage girls - right now in this day and age - have a higher than normal death rate, higher rates of disability, and higher rates of poverty and disadvantage.
One would have to compare the figures from the Tuam home with those of births among disadvantaged households in Ireland, for a true statistic picture.
As an Australian, I do assure you that in all sorts of places there are anonymous graveyards for the unnumbered dead. In my country, they are found beside the old TB Hospitals, and places like that. There are lots of them. It is not shameful. They died and rest in peace. Often the land is later recycled for some other use.