Again, I like your stills. You probably explained it elsewhere, but how are you getting the frame grabs from the BMPCC? Are you grading with Lightroom?
Can you drop box me an original frame grab to try in Lightroom? Maybe one of the first two?
"One camera. One lens (12-35mm f2.8)" That is exactly why I enjoy the Sony RX100 so much (even though it won't do RAW video). It provides 28-100 equivalent zoom. If I understand it right your lens on a BMPCC would be 36-105 equivalent. Mine fits in a (zippered) "travel shirt" pocket!
Frame grabs are a unique art form, or technique, I had never thought of until you posted one long ago from another camera. Since then two of my favorite photos of my granddaughters are from p60 footage. One is a perfect moment of windblown hair on river boat ride. The other is a nano second before striking a baseball. Both are enlarged and framed. No, they are not as tack sharp as a "real" photo, but they please everyone that looks at them.
The potential for frame grabs is one of the reasons I never take my cameras out of the 1080p60 mode.