Thank you to all the advice, particularly from those who actually read my post
I don't have the 16-35L, and this would be a great lens for it. I don't have the cash for it at the moment.
RLPhoto - no idea why dance receptions are relevant to this...
LOALTD - I understand the Sigma 35mm f/1.4 is pretty good, but I have the 35L and so have no compelling reason to buy it. I keep reading about autofocus issues, even with the Sigma, and so went for the 35L instead and have been pretty happy with it. I was hoping for the 35L II but this seems like a fantasy.
TrumpetPower! - I do have the 40mm pancake but hadn't considered it - 2.8 is only one stop faster than f/4, and with the high ISO capabilities of the 5D3 I would choose the 24-105 f/4 over the 40 f/2.8. The reason to go for the primes in this environment would be to get substantially more aperture. I love the colour rendition of the 24L. I do take your point about it being more easily passed off as amateur though. My 40mm stays on my camera a lot of the time when I'm doing street photography as it is less conspicuous.