How to key in and display date with hours and minutes into Oracle SQL Developer?
After some more poking around I found the right preference setting (screen shot below).
Under "Tools -> Preference" there is a Database:NLS node you can configure. The setting I changed was "Date Format", which I changed to 'YYYY-MM-DD HH24:MI:SS'.
I had to restart SQL Developer in order for these changes to take effect. After that, dates display as I want, and the input mask on the GUI also allowed me to edit time.