We were in similar position as OP a couple of years ago. Then management issues were very much apparent - acting head etc. However, the school has much more stable leadership now that it is part of a Education Trust. We also didn't have a great experience on the open day - very pushy parents and rude PTA volunteers, who weren't keen to discuss the school. DD found the girls not v friendly on exam day. But there was lots to like - facilities, results, quality of teaching etc.
Moreover, Nonsuch has changed a lot in the last 30 years or so since I attended; back then there were 120 girls in a year, v few girls outside of the LBS and having tutor was rare and only for girls who were struggling!
Before offer day DD stated that she didn't want to go to Nonsuch and would prefer Rosebery. In the end we were offered Rosebery on offer day and a wait list place a couple of weeks after. But we opted for an indy as we agreed with DD that it was the best fit and she is thriving. Ask your DD what her preference is - she may already have a firm view.
I would also look closely at the transport; the year DD would have started Nonsuch, I commuted via Cheam to work and trains were constantly cancelled etc. Many of the girls changed to the bus as a result, but I think it is only every half hour.
As as most of Epsom is in catchment, if you have an OC place I am assuming you live outside the centre of Epsom (if you live in Epsom). Two years prior to applying we moved appx 0.5 miles within Epsom and our new address was OC. Too far to walk to town centre (40 mins), so either a half hour bus or lift to station to then catch a bus or train. For DD to attend Rosebery she would have only needed to catch the bus or get a lift to the school (nearer than the station). For us Nonsuch really had to show a lot of 'added value' to merit the extra journey time and potential stress to DD of trains and buses not connecting.
Do you have any other DC? We have other DC to consider and DD's younger brother was unlikely to get into Glyn. Nonsuch would have worked with Glyn or Sutton Grammar in terms of pick ups, but our state back up for him was in Leatherhead!