I think there is something in the way the measurement is being done that is throwing off the result, simply because 300mV of hum on the output would make the amp un-listenable. Your description is of hum that is there enough to bother you, but not something that completely overwhelms the music, so I will assume that the hum you are hearing is a couple orders of magnitude lower than 300mV.
What we often find when trying to do AC measurements that that the test leads themselves can pick up stray hum. What I would suggest is to make that AC measurement again, with the red and black test leads twisted together (this helps to reject interference) and with the black test lead clipped to the negative terminal of the headphone jack, right next to the red test lead clipped to one of the positive headphone jack terminals.