It works!!!
For the record, here's what I did:
- On the local system, create/edit $HOME/.ssh/config and add "ForwardX11 yes"
- From the X desktop, ssh to the remote server
- Run the X application on the remote server from the ssh instance
And it just works!
I didn't enable anything about terminals and I haven't missed it yet, but that might be needed for something this application doesn't do.
Thanks, guys!