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After updating Cycle.js's state management library I was able to build and publish cycle-native-navigation-web (alpha version). So far it only supports a tiny subset of react-native-navigation, just enough to let me get started with mv desktop. But updating it will be simple from now onwards, it's just a matter of supporting different screen transitions, methods, etc. The core logic is built.
So I put cycle-native-navigation-web in Manyverse, and after a few hurdles, it works! Here's an example of a screen transition, from the Welcome screen to the Central screen.