So… I was explaining what inverted phase was to a friend of mine. Said he swapped the DAC cables around because he was too lazy to pull his speaker amp out from the wall to switch cables around after mixing up L/R. Told him it was fine as long as the positive and negative leads were in the right spots.
Then I thought, wait a minute, I had to swap DAC channels with the JotR because the headphone pinout was flipped. I had better not have been listening to inverted phase for two weeks! Looked it up, and yessir, the phase is also backwards. So it looks like a custom adapter is a must for non RAAL headphones on the JotR.
Here is a link to a headphones.com forum post about the pinouts in case anyone is going down this route. I ordered a custom adapter from Hart Audio today. Gave them the pinout blurb and asked for some heat shrink around the amp side.