I own and love the 135/2. Never shot the 100/2. I don't necessarily agree with the idea that fast glass is overrated. Im not sure I have seen the color, contrast and sharpness from slower glass that I have seen from fast glass. But thats for another post.
The 135 f/2 is an absolute scorcher. Owning a 70-200 f/2.8isII I didn't think I needed one but picked one up a few months ago. Truly amazing.
However, to give your shoulder a break during your long days on the road, had you considered the 70-200 f/4isII? They're very light, sharp wide open and would leave you with the flexibility of a zoom plus have very handy IS. See if you can get a test drive of one. It's a lot of photographers favourite lens.
You're right there...few photographers would have both. But I can't answer this for you. Most posters seem to be pointing you towards the excellent 135 f/2 so I just thought I'd toss an alternative (70-200 f/4isII) into the conversation. Why not try a pre-owned 135 f/2 and if you find it does not suit you, re-sell and you probably won't lose a penny on the deal. It's a very easy lens to move second hand.
Since you mentioned you're planning to use it in low light conditions, I'd vote for 135 f2. I own one and it's a great portrait lens, not heavy, so you could carry it the whole day without the tripod/monopod. I've never owned 100 f2 but I've heard a lot of good stuff about it too. Although it's not weather sealed, it's much cheaper that 135 f2.
It may sound silly, but have you considered Canon 90 f2.8 TSE? Maybe some of its owners can comment on it based on their experience but I think it should add some creativity to your photography.
Good luck with your choice. I think all three lenses you mentioned are excellent!