UPDATE: Success! My MHL is now working again! I didn't factory reset or anything. All I did was try plugging it in again, though this time I plugged the power charger into the adapter. It still didn't work at first, but the phone display had rotated to landscape, and the HDMI logo was in the task bar. I unplugged and replugged and it finally worked!
So it appears that the adapter won't work unless the power is also plugged in. I tested this by unplugging the power cable while it was outputting over HDMI, and my TV went black. Plugged the power back in and it came back on my TV screen.
I wonder if this has to do with the new power saving features in the update. It would make sense, since it's a big battery drain, especially if you're playing videos.