Appreciate all of your advice (even if you don't all agree). Since it's our first time, we'll try to make it as simple as possible. To be conservative I could book a later train in advance and the change to an earlier train when I pick up my ticket... or?

The Hongqiao-Hangzhou route does have 3-4 high speed trains per hour, so there are good chances of getting a seat on a weekday afternoon.
Any difference between Hangzhou main station or Hangzhou East? East station seems to be a little farther from the Hyatt, but I'd rather be on the next available train.