From what I gather, every time a sound plays on Ubuntu through HDMI (whether it's a system notification sound, audio from a game, audio from a video, anything) the audio has to be combined with the HDMI output.
This results in the HDMI flashing black as it re-syncs. It's only about half a second, but it can get rather distracting.
Now, I noticed something interesting. If one audio source is already active (like playing a video), and another audio source chimes in (like chat notifications) they come through just fine, with no re-syncing of the HDMI video feed.
This tells me that all we need to do is somehow keep the Audio output active. Either by telling it not to de-combine when not used, or by sending a constant audio signal to output (dead air?).
So essentially, I need to keep the audio active through HDMI right from the moment of startup.
I have no idea how I'd do this.