Canon 24-70mm f/2.8L II or Canon 24-105mm f/4L IS + Sigma 35mm f/1.4

I'm upgrading from a 60D to a 6D. I am debating between purchasing either a Canon 24-70mm f/2.8L II or a Canon 24-105mm f/4L IS with a Sigma 35mm f/1.4. In terms of cost they are similar (though I'd need to sell my 77mm filters and buy some 82mm ones with the 24-70). Either choice will be paired with a Sigma 85mm f/1.4 (and macro and f/4-5.6 telephoto lenses). I do general walkabout photography, but I also I often shoot at events, sometimes with a flash, sometimes without. I also take quite a few shots of friends' kids (0-4y.o.). I shoot a bit of video, but stills are what I do most.

Here are the advantages of each, as far as I can see:

Canon 24-70mm f/2.8L II
- One lens - no switching, less to carry
- Switching to the 85mm less frequently when 70mm @f/2.8 will suffice
- Versatility of a zoom over the Sigma
- Very high quality images throughout the range
- Better low light performance and subject isolation than the 24-105 at comparable focal lengths

Canon 24-105mm f/4L IS with a Sigma 35mm f/1.4
- Increased range at the long end of the zoom
- Image stabilisation on the zoom
- Better low light performance and subject isolation (less relevant this wide) with the Sigma 35 over the 24-70 @ 35mm
- Very high quality images @ 35mm
- Not having to sell my existing 77mm filters and buy larger ones

I strongly prefer one lens over two (less to carry or not choosing to leave one behind) and switching to the 85mm less frequently when 70mm @f/2.8 will suffice. I strongly prefer the low light performance of the Sigma 35 compared with the 24-70.

I prefer very high quality images throughout the range. I prefer image stabilisation on the zoom (including for video).

I can live with the loss of 35mm at the long end of the zoom. I can live with infrequent switching from the 24-105 to the Sigma 35 when lighting/subject significantly change.

Any thoughts that might sway me?