This is highly relevant because 400 Mbps = 50 MB/s would mean 80 second shots :D
It seems to support exFat: https://suggestionofmotion.com/blog/nab-2015-panasonic-gh5/http://www.theverge.com/2017/1/4/14145730/panasonic-gh5-fz80-gx850-compact-cameras-ces-2017
damn i got fooled by the nfs coding. this is OLD.
Well you could get a speedbooster knockof like lensturbo or whatever is best right now. And the EF 1.8 50mm plus a wide angle.
I dont quite understand why you only want to use one lens... i guess the sigma 18-35 comes to mind if you are willing to stretch you budget.
There is a really nice cctv (c mount) lens that you can get for around 30$, its a 35 f1.7 lens which is sold under different names. Its really usable. the adapter is around 5$. They also have a 25mm 1.4 which is shitty, dont buy that. You could use it for the beauty shots and some image stabilized panasonic kit lens if you want it really cheap...
I also think i would not do it although i think the bmpcc is a great camera.
If you get a 4k recorder, you can convert your 4k to a 444 10bit(ish) 1080p.
You will also have 4 times finer noise.
That said, i got the olpf for my bmpcc because moiree can be a matter of can-i-use-the-shot-or-not/ life and death and i had some evil agressive rainbows lurking around, waiting to eat my picture.
Metabones makes sense, because at some point you might want IS lenses.
Also an option would be the LensRegain adapter if youre going the EF route.
They seem to look great, have just a factor of 1,75 but a serious focus addon:https://www.bhphotovideo.com/c/product/1251088-REG/aputure_declr_mft_dec...
All that for the price of a used A6300. Awesome.
Also, you can use it as a door stopper :)