Canon 70-200 f/4 IS vs f/2.8 IS II for VIDEO

Yea, we are somewhat in the same boat.  I'm a guitar maker who figured out long ago the advantages of do it yourself free YouTube video advertising. At first I filmed myself playing my guitars. I've spent $50,000 on video and audio equipment, and haven't regretted a single purchase, I've only made money from it.  At times though I have to admit I schedule shipments from Adorama and B&H to arrive when my wife is at work.  To her thank God, all lenses look the same. Although when the 80D arrived a few months ago, she asked me why I needed another camera.... I though that was a silly question. 
What at first was a basic set up and knowing nothing, to more than a decade later and still knowing nothing.... ha!
One other consideration is getting the 70-200 f2.8 version I, I'm also considering that if I run across a good deal, and have a buyer for my f4. I just find that the added stop is absolutely essential especially if you are going to shoot solo guitar or music videos indoors without blinding your talent. 
I love the soft look of the 5D III.  Personally, I find the sharpness of HD and 4K on people up close to be too much, the 5D3 excels in portrait shots.  Thus the reason I've started using the Tiffen Pro mist filters to soften the detail in skin. So I find the 5D3 to be great for that. My problem with the 5D3 for video is I often forget to change the shutter rate, picture profile etc. from the photo settings which I use more than the video these days.  With the C100's everything is right there at your fingertips, and under pressure of setting up matching exposure and color balance, audio etc. it's far less stressful than the menu diving and trying to recall if I remembered to do this and that on the 5D3
Between the 5D3 and the 80D I've had good results with the 80D for video. I got it specifically for use on a gimbal because of the AF.  The 5D3 of course doesn't have AF. The image of the 5D3 I find harder to match with the C100's because it seems the image is more saturated than the C100's, and the image of the C100 tend to be warmer where as the image of the 5D3 is greener.  Setting the white balance to the same kelvin on both cameras doesn't yield the same result.
 This video was the first time I used the 80D and felt it was a better match to the C100's than the 5D3..... probably just got lucky. That said, I'm not a professional colorist and others I'm sure would have less problems matching cameras.  
I dont like the photography side of the 80D after working for years with the 5D3.  The images are much noiser than the 5D3, and I just find the images far more pleasing with the minimal effort I put in than the 80D. Of course I love the flip out screen and find it hard to live without. But for what I do I don't see the point of a crop señsor camera if you have a Full Frame for photography. 
Anyway good luck, and HODL on to that 2.8!