Just realized that I have a CEntrance HiFiM8, which is a DAC/amp with selectable output impedance (1, 2 and 10 ohms) and balanced, single-ended, and optical outputs. I drove it with digital input from the Lightening connector of the iPhone 5.
I tried the Grado GS2000e in both single-ended and balanced mode, comparing sounds on both the test music that I use to evaluate soundstage and positional resolution, on orchestral work where a wide angle and variety of instruments are present, and on some smaller-ensemble music where I heard some surprising depth of sources, e.g., drum set with sound having dimension toward/from the listener.
In all cases, I could not distinguish any difference between single ended and balanced. I could not form a preference because I could not hear any difference.
In the past, when I got a balanced cable for my Sennheiser HD800, I had heard a difference between single ended and balanced, both in tonal quality and in instrument position, on my Sennheiser HDVD 800 DAC/amp. So I sort of know what to listen for, but here, I heard no difference.
Were you able to use the HDVD 800 DAC/Amp or just the HiFiM8? I too own the HiFiM8 and if I am correct; it has a xlr output that is not actually truly balanced. It just has the xlr connection.