Airplane Seat Power Ground Loop?

clearthink the problem does not occur outside the airplane ie when it’s plugged into a land-based power source.

Also, I used another dac (a THX one) and got the same problem except the problem doesn't go away when I touch it.

I don't know the answer but your first world problem made me smile.  And reminds me of having to hold the TV antenna when I was a kid.

exactly what I thought

Have you tried a mophie or other brand portable battery charger to extend the laptop life?

Interesting. 

When I worked on sensitive equipment, I had to use an AntiStatic Wristband to ground me to the workstation.  It looked like the Twist 'o Flex watchband. Connected that wire to your dac.  Some antistatic band did have a like a 100M ohm resistor in it, which we had to check every so often.  Idea is to Bleed off the charge.  Not current thru you.  Or maybe put a ground lead from your headphone out to the padding of your headphone.   I'll choose my wrist thank you.

Why?  I don't know.  Guessing on it.  The USB power ground might be floating and not part of aircraft ground.  Like that 100M ohm resistor, your butt is it.  You could take a jumper lead from your dac straight to a metal surface of the airplane.  I you get a smoke from your laptop or dac or a big arch and the airplane stop working... hey! sacrifices must be made in the name of Science.