[madbrain]

Is there any chance one could use Kodi on the Pi3 to stream the audio to the Chromecast audio instead of HDMI, while still streaming the video over HDMI ?

Not likely. Kodi is all open-source, and Chromecast is proprietary/closed software from Google.
Those two types do not mix will in ourview. Thus, Kodi has no support for Chromecast, for audio or video.

Yes, I'm aware it is closed-source. Are there other streaming devices that would work for my use case ? Say, if I had a Raspberry Pi with PiCast or equivalent, would there be a chance for Kodi to use it as an audio device when playing videos ? I realize there would likely be some audio/video sync issues, but those could be hopefully adjusted manually with some delay parameter.