It turned out to be pretty easy. After I arrived, I took the maglev (I had too...) to the #2. Took the subway to Nanjing road. Walked the road (and must have had a sucker tag attached for all the 'offfers' I received.) I walked to the next station and continued on to Hongqiou.
There I tried to buy a ticket for a train that I thought left in 15 minutes. The guy told me that I couldn't (I really need to work on my Chinese) and I got a ticket for a train that left in an hour or so. It made just about every stop, though the first class compartment was pretty empty.

I got to Nanjing station, and easily made it on the subway to my hotel.

For the return, I had the ticket purchased in advance.

I went from Nanjing to Shanghai main station. There was one stop and it took about 90 minutes. From there it was another 90 minutes to the airport. (But that included a lot of wandering around aimlessly at the train station and a visit to the Maglev museum.) I was at the airport ridiculously early.