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Funny, I am trying to get the answer for the exact same question.
First of all, resolution. The A7s' resolution is fine. I can further improve it with the Shogun, but as I wrote, the resolution should suffice.
Then the colors and gradability. The colors are few (8-bit). In theory, the A7s can depict almost 15 stops, more than even the 4,6 Ursa Mini. But only at the native ISO of 3200 (that's why this is the default ISO for S-Log). 
S-Log fits to landscapes, but imo not for skintones (too few to make them look alive). So until further experiences, I stick to autumn leaves then, shoot only at ISO 3200, use only WB 3200, 5600 and 6500. I need to buy fixed ND filters, because with such high ISO, ND faders all destroy the colors.
I'm not finished with my evaluation, these are my initial findings. I hope I can get close to this look ...

Sony's plan cannot get any clearer:
Get an A7rii for high res stills,
then an A7sII for low light video,
then an FS5/7 for actual work, 
and next year start all over again.   

I'd be surprised if it were reduced that much, Sony makes big claims with things like RS and DR that never pan out. My guess is that's not the case, which is why it wasn't highlighted in the rollout - because just 8.3ms would be huge news.

Sounds correct, unless there is a catch with the "full pixel readout". 
It will be interesting to see why Sony decided not to advertize one of the most important improvements if it is indeed 8.3ms also in FF 4K mode. 

I doubt slog3 is going to be better than slog2. If anything it will make it worse for skin colors since there are even less values assigned in mid gray level. Increasing the dynamic range with 8 bits is just not good for skin colors. I wish they had included 10 bits. But that might have been impossible with the current thermal envelope of these cameras. 
Now, the only difference between this and A7rII for my use is the better high ISO sensitivity. Maybe the overheating too since I doubt they released a video centric camera with overheating problems. 

If you have the opportunity to use a C100 MkII I would do it. Hands down a documentary superhero camera. I intercut the footage with 4K alot, and the resolution holds up well.

I'd recommend you should go give Oly a hands on try.  The stabilizer on the EM5II is at a whole 'nother level.  Crazy good/cool.  At the very least it can be a useful Bcam for specific situations.  Driving in a car, sailing on a boat, scooting along in a tuk-tuk.  If you want or need it, it's a very very wonderful tool to have in one's arsenal.  Or, grab a cheap EM10!
Anyway, all these cameras listed here are pretty cool; can't go wrong, really.  

Yes we are shooting mixed 1080p/4k doc material now with the A7RII, GH4, D810 and 5D3. Unfortunately I don't have releases to post any samples. Before getting the A7RII and 28-135 f/4 cinema lens, I looked very closely at the C100MkII. That is a great camera and I love the built-in features (ND, XLR, etc). The C100 deploys very fast, which is important for field doc work. By contrast it takes 10 minutes to rig a DSLR with EVF, brackets, HDMI, cable protectors, etc.  It's fragile in that state and every time we change sites we must decide to de-rig it, have someone hand hold it or risk balancing it on a car seat. However the C100 is essentially video-only and I wanted combined stills/video, plus we do lots of time lapse and that wears out a DSLR, whereas the A7RII has a non-mechanical silent shutter mode. 
We'd have used regular Canon L lenses on the C100, which means no smooth motorized zoom. We have all kinds of focus aids (sticks, knobs, Zacuto rigs, etc) but they can be a  a hassle for field work. 
We won't distribute in 4k anytime soon, but shooting in 4k for 1080p distribution has advantages.
- Allows looser framing and fine-tuning composition in post
- In many cases 4k frame grabs (which are 8 megapixels) are usable as stills, which saves switching between still & video mode or using two cameras. We shot a project two weeks ago which the customer said was video-only, then afterward they wanted stills. We fortunately shot in 4k so the frame grabs were good enough for this purpose.
I always use the battery grip on the A7RII, which (a) Makes it a lot easier to hold with a big lens on the camera, and (b) essentially eliminates battery life issues. There is functionally no difference between shooting video with that vs the 5D3. In both cases you have to change batteries at least once or twice per day depending on shooting duty cycle.
Last weekend I shot mixed 4k video & stills all day in direct sunlight at 95F ambient temps, and the A7RII did fine. OTOH it will definitely overheat and shut down if shooting non-stop, long-duration 4k, but that is not a common usage for us. We would never shoot a classroom lecture at 4k, and a 30 min. interview is very rare (for us); not sure we'd shoot that in 4k either.
For me the biggest negative on the A7RII is the fiddly, consumerish user interface. I am frequently changing it in/out of Super 35 mode, and it is maddening this requires diving into the menus every time. Formatting a memory card takes a long time, and invoking that also requires diving into the menus.
The GH4 is a great camera with much better UI and lots of aftermarket support. But we shoot mostly full frame so haven't fleshed out the GH4 config. In Super 35 mode the A7RII is very good at low light video (better even than the 5D3). We do lots of existing light shooting so that's important.
The Sony 28-135 lens is a good match for A7RII video work. The smooth motorized zoom and ability to pop between manual and auto-focus by sliding the focus ring forward/backward are very handy. The lens and camera are expensive but still cheaper than a C100MkII body, plus you get 4k and 42 megapixel stills. That said if it were not for that lens I'd have probably gotten the C100.
We are still evaluating various post-processing and color profile options for matching 4k from the A7RII with the other cameras.

I just did a 10 minute corporate thing with a gh4, 5d, and an EM5II. 
If you shoot clean and expose properly you can get em to match pretty close in the color grade, but you need to be patient at it. 
The GH4 looks like it has more resolution, because it does, but you can't really tell the difference in the final online delivery unless you're looking closely. 
FWIW, I shot for a month last summer in Indonesia (hot!) with LUMIX and Olympus gear and it held up fine. I got tons of great video and looked very unassuming while doing so. 
I'd recommend the Panasonic cams. Cheap and really nice video IQ.
Not sure how particular you are about having the GH4's 4k, but the EM5II's 5-axis stabilization might actually allow you to capture better shots on the fly.  That built in stabilizer is something else.... Plus, the camera is weather sealed, which is nice to have; something else to consider. 

If size is a concern and you have Canon glass, the GH4 and the A7s are probably the best options since you have electronic adapters and speedboosters for both. You can get something like the A5100 as a B-cam for the A7s that will also serve as a backup, they use the same batteries and it'll take 24mp stills. I keep one in my bag at all times, usually with the 10-18 for great UWA shots and handheld cutaways. GH4's cost less than the A7s, you could easily get a 2nd one or a cheap GH3 as a backup. Lots of options.

Cross the Ursa off your list if you need it in the next couple weeks, even if it does drop early (B&H lists it at Oct. 22 now). I own and really like the A7rII - its a stills and video powerhouse, but if I were buying a camera to shoot a doc and already had Canon glass, the C100 (mkI or mkII) would top my list. That's what the C100 was made for and it does the job really well - dual pixel AF, C-log and so on. Unless you want something smaller.
I like the smaller form factor so for me - get a couple GH4's or a pair of A7s' (used prices are in the $1700 range). Sriracha the movie was shot mostly with a GH3 and the Panasonic 2.8 zooms (stabilized), it looked good to me, but I'm not hyper critical and its an entertaining story that was well done. The IQ from the GH4 with 4k downscaled to 1080 and V-log will be much better than the GH3 - but it will probably surpass what you've already shot as well. But so would the A7s and C100. Just my .02.
Good luck.

The Doc Searching for SugarMan (2012) used all sorts of different camera footage - he ran out of money & had to resort to using his iPhone (not one of the new ones, but one circa 2010/11) to film a portion of it.
So might be worth doing some research on what cameras they used & the tricks they employed to mix'n'match different quality footage. The one thing I do know about the iPhone footage, was that he used an App that simulated s16mm style footage. Must be lots of tricks out there...

I have this one.
Can be had with various connectors and it also has a regular power outlet so you can use whatever cable you want.
It has a regular 1/4" screw to mount on a regular cage, arm, what have you.
It can also be bought with clamps.
I you zoom in on the left side on the eBay picture you se the second outlet which is a standard power outlet.
http://www.ebay.com/itm/Blackmagic-BMCC-Camera-Battery-Mount-Plate-Power-Supply-Adapter-For-Sony-BP-U60-/370877762077?pt=UK_Camera_Battery_Grips&hash=item565a098a1d

I have a a7s and a SMAD-P3 and have asked Sony about this. They said they might make a SMAD-P3 with a 3.5mm input for ch.2.
I can see that you would need more advanced audio circuitry to control two different inputs, but you could always hope.