Does anyone have any information from previous years as to what rank your DD needed to achieve to gain entrance to the school?
Not really. You are correct that you don't need to be in the Top 150. You find that there are many candidates who are applying both to Nonsuch and to TGS and they will ultimately choose one over the other and hence will allow the cutoff to move down.
However a good score at Stage 2 is mandatory as not all Stage 2 candidates will be above the final threshold.