A bulky solution is the Tascam DR701d.
http://tascam.com/product/dr-701d/ For HDMI Video Signal: 5D MK III --> DR-701d --> Video Assist
For Audio: 3.5 mm Mini jack from microphone (Video Mic Pro of the sorts) to the DR-701d and output back to camera. The DR-701d and Camera are recording same audio now, individually, you can send the audio to HDMI out in the DR-701d
From Tascam "The recorder’s audio signal can be sent to an external recorder using the HDMI output".
You might need a big rig for this, but the 701d has Camera mount on top specifically for DSLR of the size. Your camera rig will be a behemoth, but isn't that a lovely toy to have
I am actually considering this route.. Not just for getting audio to the Video Assist, also because I need a field recorder.