I agree. Go for the GH4 with the Shogun and Metabones Speed Booster. Shogun on GH4 will give you 10bit 4:2:2 recordings, A7s 8-bit. The Speed Booster will give you the extra stop and changes the cropfactor of 2,3x (4K) to 1,63x.
I have worked a lot with the 7D and 5D III and switched to GH4 last year. It can be a difficult choice to change from Canon to Panasonic, but I do no regret my choice. I do recommend to buy a Metabones Speed Booster (EF / M43). This will give you an extra stop and will also change your FOV. The crop factor of the GH4 in 4K is 2,3x and in 1080 it is 2x. The Speed Booster will reduce that wil 0,71x. Your GH4 will become more of a super 35 camera and will give your more choice in lenses as well! And by the way, the firmwire of the GH4 is so much better and more stable.