Not sure if there is anything commercially available for taking the Black Magic cams underwater, certainly not with a live feed functionality. Conflict of interest alert-we do live feed/remote control of HD action cams at Spot X Underwater Vision (mods, remove if this is not allowed) and we have a number of customers add one of our units to their ROV, but I can certainly offer some advice for people going it alone.
I use Hero5 Black and Garmin Virb Ultra 30 cameras on board our BlueROV2, both with image stabilization on (available up to 2.7k). The downside with shooting 4k is that the cameras overheat quickly, especially in housings, so you may only get 15mins of footage before they shut themselves down.
In regards to a live feed, it’s not easy to do in HD form. If you can get by with a composite feed (500TVL) this is how you do it.
**Hero 5 -**You will need to convert the HDMI to AV using a powered adapter for the Hero5. These are readily available, but need 5v.
Hero3/3+/4 You can take live composite feed straight from the USB of these cameras using the correct connector, you can find these on Hobbyking or any FPV store.
Depending on RF noise, you can actually run an AV live feed directly over a spare twisted pair. Just use some screw down baluns to match the cable coming from your camera. I haven’t tried it on the BlueROV2, but it may work, composite feeds are pretty robust, and because they are analog, they just degrade, they don’t “fall off a cliff” like digital signals
If you use a Garmin Virb, you can convert HDMI to AV using the unpowered boards offered by HobbyKing.
If you need a remote trigger for the GoPro (start/stop record from the surface) this can also be done but that’s probably a bit off topic, let me know if you’re interested.
FYI…Rob, no doubt you understand the benefits of 4k, but for those reading who may not, and be wondering why bother…it’s true, for most people, 4k isn’t worthwhile for viewing, 1080 is “good enough”…but most importantly, especially if your 4k camera is flying blind, consider that in post-processing you can “zoom in” on that 4k image up to 200%, crop, and still have a 1080 finished image.
Another cool editing trick, is that you can make it look like you have multiple camera angles, using just the one camera, eg some wide angle views, some close ups etc. If you can shoot in 4k, and export in 720p, you have a lot of options