So, I truncated all of the classes in the source File Geodatabase and then copied/pasted into SDE. This worked.
Then, after putting some data into one of the classes I found problems creating a spatial index on that class. At one step along the way I got an error message pointing to an issue with the Oracle object sde.st_spatial_index. I tried granting EXECUTE on this object to all users, including SDE and tried granting permissions to users per the SDE Admin guide. Still got errors creating a spatial index.
It may well be that the spatial index problem was what was preventing me from performing the copy/paste with a populated File Geodatabase in the first place.
At any rate I found it best to just start over with the SDE database and so dropped all users and re-created the Enterprise Geodatabase. Which seems to be working OK.
Ed