New Headmistress? Jane Gandee has been there since 2010. She appears not to have left, so what new Head?
I think people who write about independent boarding schools, need to understand the culture of schools in this sector. They all have pretty large numbers of overseas girls who board and a good number of whom will do STEM subjects. What is wrong with that? Any girl could do well at the same subjects if they chose to do them. Many boarding schools would have closed if there were not overseas pupils. Their money is vital so it's a bit rich to complain about them doing well.
St Swithuns is not overly selective. Boarding schools offer a wide experience of education and RG and Oxbridge is not everything. If the overseas girls do well, what is to stop any other girl doing well? It just may be that the brightest girls are not in a particular year group but that will vary year on year. Where my DD's wsent to school, plenty of bright girls did not get an offer from Oxbridge. Some did not see the "value" of RG either and chose to do specialist courses elsewhere. If you do not know the girls, it is hard to say if they should have done another course or not.
Bullying should be dealt with, of course, but show me a private school where there is not some degree of favouritism? In schools I know it tends to be about parental donations and involvement with the school. The daughters of old girls, for example, tend to be looked upon favourably. You just have to get over it and do not expect it to be better anywhere else. They probably have an inner circle of larger donors who get invited to special dinners etc. and this will include current parents.
I am sure you will remove your child if you do not like it. I guess maybe you already have?