Meanwhile, I also checked the reset logic, which I suspect to be quirky.
The A3000 uses a PST518, a small 3-legged IC which looks like an ordinary transistor, but monitors the +5V power line to assert a _FAIL signal when it's too low.
This capture shows what happens when the power supply is switched off: _FAIL (above) drops sharply when +5V (below) falls below 4.4V. Looks good.