this is from my mate that lives on the grounds. hope it helps as I know the detour that you are on about. I have scoped out a fair few routes around that area so give me a shout if you want any.
Route of least conflict, but you will technically go through main paths and houses on the grounds. Back avenue I believe is technically a right of way, but as it is a school it is not a right to roam. Over covid and school term it has been advised no right of access, which i think is sensible enough. But we are moving away from Covid restrictions and it is now the school holidays. I’m sure certain indivisuals will ask you to stop, question you, and advise against doing it in the future. But that seems to come from a small minority of private land owners/managers.