The direct highspeed link from Hangzhou to Beijing via Nanjing is supposed to open July this year. One of the stations, Lishui, will actually be very close to NKG while Nanjing South is also not far from that airport (Nanjing Lukou Int.). Should be less than an hour for Hangzhou - Nanjing area.

At the moment, my best bet would be to fly from Shanghai. No guarantee when your domestic HGH - PEK flight would arrive.