Here's a simple DIY way to add an HDMI Cable Pinch to one of those Gini Panasonic GH2 Video Cages [Thanks Asa]. You could use this same technique on any of the other cages offered by Gini, and I just noticed that Gini is also offering a specific cage for the Canon 5D Mark III if you need all of those mounting points. Check out the Gini gear on eBay (Click Here).
Gini Rigs Canon 5D Mark III Video Cage