Update: Turns out it is possible, with a little trickery, which just needs a 2nd login on the remote machine.
0 start a ScreenSharing connection to the remote machine
Connect To: user1@remote.machine.edu
1 initiate a second connection using the Connection menu, but specify a different username:
Connection -> new with
Connect To: user2@remote.machine.edu
2 change the "Name:" field back to user1 and enter the pwd
Name: user1
Pwd: mysecret
This opens up a second window connected as user1, which can be positioned on the 2nd screen of the local machine.
3 switch the 2nd window to Display 2 ( on View menu, or Displays pulldown )
The only problem is cutting/pasting between the windows usually freezes the remote connection. This may be because my local machine (a 2011 iMac desktop) is running MacOS 10.13, while the remote machine is running 10.15.3, and there may be some miscommunication between the versions. (If anyone else tries this with 10.15 on both ends, please post whether this is still a problem.)
FWIW: when the connection freezes, it can be reestablished by opening an ssh connection to the remote machine and restarting the ScreenSharing daemon with
sudo launchctl kill KILL system/com.apple.screensharing
(KILL should probably be SIGKILL, but KILL works.) This is easier (for me) than closing the ScreenSharing windows and re-establishing the session. It takes a few seconds for launchctl to restart the daemon, and then the windows become active again.
