No, that's not what you said. You said that a single-ended cable could be connected to a balanced output, which is not correct. That cannot work. Regardless, that is not necessarily the issue here.
Yes, the Masters are balanced from the earpieces to the female 3.5mm connector, but the R- and L- wires are tied together at that point because it is a TRS connection. It is a TRS connection because the supplied cable is TRS on both ends. TRS and TRRS connectors are not interchangeable. You cannot connect a TRRS male connector to a TRS female connector or vice versa. Therefore, since the female connector is TRS by definition, you will never be able to achieve a true balanced connection from the earpieces to a balanced source because the earpiece grounds are common at the y-split.