I think having 35mm, 50mm, 85mm, 135mm is too much for street photography, at least for my taste. If I were in your shoes, I would have thought of the below options:
1. Canon 24mm f/1.4L II + 50mm f/1.2L: Expensive combo, but when combined with your 135L you'll be having the tools to shoots almost anything on the street. Both lenses produce quality images, built well, and weather sealed.
2. Sigma 35mm f/1.4: 35mm is an amazing general focal length. Combined with your 135L, you shall be having a light weight combo that covers almost everything you may need on the street. The Sigma 35mm f/1.4 brings out quality images, built well, and cheap in price.
3. Fuji X100s: I have used the X100 before, and I can tell it's a very nice camera in terms of image quality. The camera is nicely designed, small in size, and has a lens equivalent to a 35mm f/2 on your 5D Mark III, which is a focal length I love personally. One more advantage will be that you'll have the chance to keep the 135L on your 5D Mark III all the time, and enjoy having 2 cameras ready for the shot instead of one.
4. Fuji X-Pro 1 + Fuji 35mm f/1.4: Same benefits as with the Fuji X100s. According to all reviews I read online, this combo produces Pro level photos. The combo is smaller and catches less attention than a DSLR would do, which is a great benefit for street photography.
5. Canon 16-35mm f/2.8L II: Built well, weather sealed, produces quality images, and versatile. The focal range is very nice for street photographers, and will make you never worry about shooting in tight places.
I prefer wide angle lenses for street photography, just use my 135L when I feel like shooting candid shots from distance. I own the Canon 35mm f/1.4L lens, long before the Sigma was announced, and it's my go-to lens for almost all types of shoots. My copy is sharp, which made me feel no need to replace it with the Sigma. But if I were to buy now, I would go for the Sigma for sure.