Since this was posted on 2006-03-02, we have come up with a third solution for interrupting the ground loop. See Isolating Battery Eliminator
What's happening is that the switching power supplies inside the UM400 transmitters create noise on the ground plane. This noise then has two paths because of the dual ground paths: one through the DC power and one through the audio ground connected by the mixer. Although mixers often have a transformer balanced output, some transformers have capacitance which can couple pins 1 and 2 to ground at high frequencies (such as hiss from DC switching supplies).
The solutions to this are as follows: