RSS stuff is awesome.
In addition to the BH-40 that so many others have rightly suggested as would be perfect for your setup, let me also recommend the RSS L-plate for the gripped 5DIII. Said L-plate literally lives on my camera. Believe it or not, the grip is actually more comfortable in the hand with the L-plate than without. And stick one of those little 1" clamps from...Kirk? -- I keep forgetting...anyway, put a mini clamp at the end of a BlackRapid strap, and fasten the clamp to the left side of the camera, and you've got yourself an awesome walkabout setup. The 24-105 balances the whole thing perfectly, and it's all superbly comfortable.
One other tip: you can get USB cables with a right angle at the small end; those work much better for tethered shooting than trying to cram a regular cable between the bracket and the clamp.
I have this clamp to attach to my Black Rapid strap - it works great! A bit of loctite on the BR screw and it's as solid as can be.