Aha! I think we found the problem. I believe I have a rev 1 supply with a rev 2 top board.
On my top board CR27, R121, R102, R104, R105 near U28 and R70, R71 near U23 are unpopulated. Also, the firmware ROM is rev 1.4. And the board silkscreen marking has an F-1 sticker on top of it.
However, on the bottom board, U5 is populated, unlike in the teardown unit linked earlier. It seems on the new revision, the shutdown signal was changed.