Hey Luca,
Your question is my biggest issue with the camera. All I need is one more SDI output!!! Anyway, my answer will get you only 1080p to the 4k video assist. Get a T splitter for the front SDI port. I think they're like $5 at film tools.
When I have a studio build, I have my BMD EVF and my 5 inch VA split from the front SDI, and my 4k VA out the back for my AC. Then I run a wireless system out of the 4k VA.
All of the devices are powered off of D tap cable, running into a D tap splitter from Wooden Camera. The batteries I use are Anton Bauer Cine 150's (the carbon fiber looking cube ones). With all of that I get about 2 1/2 hours a battery.
Hope this helps!
~Chris