The files are usually stored in ~/.config/Duplicati.
You need the Duplicati-server.sqlite and any *.sqlite files.
I am not aware of any good workarounds unfortunately.
If you can live without having the tray-icon, you can ignore the dependency and just run duplicati-server instead of duplicati.
If you really want the tray icon, I will post a canary build soon that does not rely on libappindicator or mono. It does change quite a lot of things though, and is significantly less tested, although the core implementation is unchanged.