I have DD in year 10 at Wok and was also there on Thursday evening with her little sister hoping to start there in 2017. My eldest was also offered a place at Togs with all her friends but always preferred Wok primarily for the aspects you give. Choosing Wok was the best decision we could have made for her. It is a very caring school which imo stretches all girls to their potential and more importantly produces confident well rounded girls.
Yes the results at Togs are slightly better but it's important to remember they are creaming off the highest ability girls in the first instance. That said, in my daughters year, there are many girls who scored easily high enough for Togs but didn't chose it and results are improving yearly.
Remember also in year 9 in Maths and science girls are streamed depending on their ability allowing all to work at their pace and ability.
I honesty wouldn't hesitate to recommend Wok. My DD loves school ( unlike my other two
) its pastoral care is incredible and most of the teachers highly motivated and approachable ( no school is completely perfect ). They are not fearful of the teachers but respectful which i particularly like.
In terms of the grounds i am a bit confused - it has a huge area of playing fields and sports courts and the new multi sports centre will be open in time for your daughter - or are you talking about the Sevenoaks annex ?
Good luck with your decision hope you find the right fit for your daughter.