You could probably play a short audio stream with roAudioResource as a wav file - I haven't tried it during video playback, but perhaps with some short 'notes' you could make some single-track MIDI type music akin to early pc speaker sounds.
Have you considered synchronizing two roku devices and two TV's - one to play audio while the other plays your video, or to take the optical audio from one roku and the video from the other roku with ECP to sync them?
Perhaps by plugging in the headphones into a roku 3 to activate the 'private listening feature' you could effectively mute the audio currently in your video. And no, I'm not interested in investing time to investigate this for you - even for money - just too busy. I'm just throwing out some possible ideas.