Convincingly simulating natural light is one of the more difficult tasks in photography, & while the fundamentals of lighting are the same for stills, & motion, the needs, & tools, can be very different. I'm a huge fan of natural light, but maintaining continuity generally means having tools to emulate, or supplement, it.
Stills photographers have a go it alone mentality, whereas motion is generally much more collaborative. There's much to be praised about the first approach, however I suggest you embrace the latter. Most DP's have big holes in the schedule, & a good one could bring a lot of value to your project. Consider yourself the Director, & let the DP fulfill your vision. This doesn't mean you can't operate the camera, some Directors do, though usually not for the entire project, but your focus should be on the actors' performance, & the story.
When choosing a camera there's a lot to be factored. As you hope to utilize natural light, high ISO, & DR, would be among my first considerations for this project. And while a 5D3 has great high ISO, it requires stopping down a whole stop more than S35, & two stops more than m4/3, to maintain the same DOF.
422 is better than 420, but not a deal killer. You'd see a bigger leap using a 10-bit or better, over any 8-bit camera, but these don't come cheap (F3 with Recorder, Scarlet, etc.) unless your willing to use a much smaller format.
And once you've choosen a camera the question becomes how are you going to support it. Anyone experienced in this field will tell you not to cheap out on the sticks, & more importantly, the fluid head. You first need to know how much your camera will weigh, then choose the appropriate head, with some overhead factored in so it's not straining.
Due to their flat mount I have numerous Manfrotto heads for use on Sliders, monopods, or such, & for awhile used a 504HD on sticks, but have moved onto Satchler as my primary head. This has made a huge difference in my operating as I can much better stick the end of moves.
Next up is how are you going to monitor. While a lupe over your camera's LCD is alright for some simple work, it's not great on sticks, or when reviewing footage with the team. You'd be better served by an external monitor, or even an EVF.
Tungsten is the gold standard in artificial light, & the most affordable, but often not practical due to heat, efficiency, & CT. If your filming nudes in winter they'd be a good choice, & in many of your examples I'd CTO the windows instead of gelling the tungstens, however in my daily work I'm much more likely to use daylight sources (Kino, & HMI).
LEDs are indispensable for some work, & there are some remarkably bright units coming to market, but color reproduction is not their strength. If absolute color is not important, or your using them just as a catchlight, then they can be useful, but unless your building a large array I don't see them as that useful for this project.
If you interested in the color issues read the Solid State Lighting Project, & be sure to view the tests. These are a great solution for insomnia.
Solid State Lighting Projectwww.oscars.org/science-technology/council/projects/ssl/index.html