How to override the Gnome 3 SSH handler?

Writing a .desktop file is not enough. You also need to change the default setting for the mime type.

You can get the current default value with

 xdg-mime query default x-scheme-handler/ssh

and can change it with

 xdg-mime default ssh-terminal.desktop x-scheme-handler/ssh

The corresponding configuration file could be $HOME/.config/mimeapps.list or $HOME/.local/share/applications/mimeapps.list depending on your OS version.