In the U.S., there doesn't seem to be a "very high" option for the playback quality. At least, none that I could find. "High" was the highest available setting. And that setting results in 2-channel playback (Dolby Surround) only. 😟
Since this is a Netflix problem, I guess I'm going to have to contact their support and find out what's going on. I've already independently verified, via iTunes-available streaming media, that 5.1 playback does in fact work on my setup as it is, so this is clearly a Netflix-specific issue and not a general Apple TV issue.
I can't tell if this issue is related to an OS upgrade on the Apple TV or not. The only way for me to find out would be for me to revert back to some older version of the firmware, and that's enough of an annoyance that I'm reluctant to do so. It's probably better to just get the issue sorted out with the latest firmware.