Take a look at the Thinktank Streetwalker Pro HD. Great sturdy bag. It can hold all that you stated. It's a backpack, though. So you have to decide if you want a backpack or a shoulder bag. Perhaps you should look into a roller bag, if you are not going on hikes in the woods with your gear. I suggest the Thinktank airport line of roller bags.
Cams: Canon 1Dx, 5D III, 60D
Zooms: 16-35mm f/2.8L II, 24-70mm f/2.8L II, 70-200mm f/2.8L II; Primes: Sigma 35mm f/1.4, 40mm f/2.8 STM, 50mm f/2 Makro-Planar T*, 85mm f/1.2L II, 100mm f/2.8L, 135mm f/2L, 300mm f/2.8L IS II, 600mm f/4L II
Support: Gitzo GT4542LS/GT2830/G2258, RRS BH-55, BH-40, WH-200