Is there a way to enable the headphone output for audio while using HDMI for video?
This is a non-answer to close the question. In the unlikely case that an actual answer appears, I'll transfer the accept to that.

No solution was found for the question as asked. By now, I doubt that anyone will ever care for that particular model of tablet, which was cheap even back when it was new. I'm still using it, as it happens, but mostly only as a PDF reader.

For displaying video, some monitors have an audio output to external speakers driven by the audio from the HDMI. It turns out my monitor had that - I'd just somehow managed to miss that at the time. I also now have a TV/monitor with built-in speakers. I still don't care about broadcast TV - I want the composite video inputs for an old PS/2.