Some quick ideas that come to mind:
1) If your film is really short, use as much as possible of the magic hour (sunset/sunrise), where the sun is not blasting full. You might be able to shoot the critical wides then.
2) During the day set up your actors such that the sun is always slightly behind, and they don't face the sun (and squint). The sun provides rim light, and you can expose on their faces. Or set them up in some sort of shadow area, whenever possible.
3) With any canon DSLR, you have to pay special attention to the low dynamic range of the camera. Ideally you find nice locations that the background is not overexposed.
4) You can use bounce cards to lower the dynamic range, but too much of it might blind the actors. (If you have big lights, you can use them too)
5) For your close-ups, you can put a diffuser between the actors and the sun.
6) Use negative fill a lot
7) As mentioned above, good ND filter is a must during the day, and probably a matte box is useful to lower reflections
They way I approach it is the following: imagine you speak to somebody and the person is moving away from you. You hear essentially a direct sound, and a sound reflected from the room. So as the person is moving further, 1) the direct sound gets less loud 2) the ratio of the room sound to direct sound changes 3) the room sound is created from different location of the point source. You could emulate what you'd call room sound with reverb and EQ, perhaps a bit dynamic processing, such as compression. In reality sound from different directions hits year ear at slightly different times, since sound has to travel different distances from different reflection paths, and this also introduces subtle phase effects. This is how your ear can decide that the sound comes from a certain direction, and how far. But to first approximation, you could just diffuse the room sound, and have a particular direction for the direct sound. If it is coming from another room, it might be completely diffuse.
In a particular room, you could experiment and move the sound away, and see how you can best emulate with mixing,EQ, reverb and compression. Finally, you could do also mix multiple recordings, such as lav+boom+room mic and carefully mix their ratios. Hope this is a good starting point.
I have both the bmpcc and the A7s. I love both.
Here's something I shot in a completely dark recording studio at f5.6
and on my reel, around 2:36 is a dark bmpcc footage ISO 800 f2.8. You can judge the grain.
hope this helps, but as others said, for low light, A7S.
The video looks great. Facing the same problem (not having a focus puller for most projects), I tested the Sony A7s face recognition+autofocus: it work much better than I hoped, seven in a pitch dark studio.