If its any consolation, I had a similar experience a while back.
I put a 4-way XLR plug/socket into the line of my AKG700s, and made up a 4-way to L+R 3-way XLR adaptor cable, so that I could swap back and forth between balanced and unbalanced o/p. I dont use headphones much, and the main reason was to try to see how much improvement I might expect from going to balanced amps for my speakers. The disappointing result was that like you, I found balanced to be much worse. The sound just did not hang together. I did of course check my connections in the adaptor, but could not find anything wrong, (though this doesnt necessarily mean that there was really nothing wrong) so I assumed this was some problem about matching MDAC o/p to the phones, and forgot about it until I did my experiments with LPS powering of the MDAC, which greatly improved the single-ended headphone o/p. Misterdog, not knowing about the above, suggested that balanced would be even better.
I was of course doubtful, but after a while I thought I should try it, and yes balanced is better with the LPS than it was before; its now listenable, but not up to the sound with the single-ended connection. I dont know where this leaves us, but the fact that you were working with a commercial cable does at least give me a bit more confidence in my own wiring.