With today's update, you can finally save your world-building progress and even exchange worlds with your friends!
There is a new button in Zen Landscape Editor - Import/Export.
When you enter that menu, you can export your whole world as a string of text, copy it, save it locally or send to your friends, and import it back at any time!
At the time, the feature is really basic, it just lets you export the world as a text, but in the future, you can expect to see an advanced save/load feature implemented, as well as postprocessing presets!