Fortunately, that problem is now fixed for new buyers; the most recent MacBooks, according to this support document from Apple, will send both audio and video out through HDMI as long as you've got a VESA compliant adapter (which most DisplayPort adapters are). Of course, I'd need to buy a new MacBook (which is much more expensive than just figuring out an audio solution), but at least the issue is fixed on the latest hardware.
My eventual solution? I was saved by Sony, of all companies. MLB released a free app on the PlayStation 3 (which I have hooked up to my TV via HDMI as well) that lets me watch my subscription without the computer. That leaves my MacBook open for other tasks, like blogging, while I watch the game. Let's go Cubs!