From the end of August to the middle of September is the high season for traveling by train since the new term of colleges and universities begins during that period. I think it is possible for you to get the train tickets Hangzhou-Shanghai because there are many trains available daily. The train tickets Beijing-Tianjin are easy to get and there are many inter-city trains daily between them. But the soft sleeper from Shanghai to Beijing may be hard to get; so you would better arrange the tickets as early as possible. You can book the tickets on this website directly.