Hi Craig. The latest software for the BMPCC 4k does activate the onboard gyro which embeds the data into the braw files for later stabilization. I also use IS lenses. The stabilization in Resolve can at times be remarkable especially with micro jitters. So this is not an issue for me
The lack of auto focus is much overhyped in my opinion. Autofocus has its own issues and I much prefer a manual approach. Indeed many lenses like my Laowa 15mm is a totally manual lens and my favourite on a gimbal. I also have seen a lot of focus hunting when people just rely on auto. (EDIT: Also the later software has improved the snap focus and vastly improved the focus assist. My friend with a Sony a7s ii was in awe of the much better focus assist and bigger screen compared to hers. She hates her peaking display. We both do doco work and she is seriously considering a jump to BM)
The real saviour with run & gun for me is the dynamic range and highlight recovery with braw files from this camera. I’m often grading footage from a variety of cameras and I find the Sony codecs in particular do not give me the same latitude.