To the OP, why not look at dedicated video cameras. They do autofocus far better than any u4/3 system and can easily do wide angle and macro on the same dive. Still $3K is pretty low budget but you might get it done.
Bill
I had been considering this option myself. Over the past year, I have seen a few Gates / AX-100 combos with multiple ports on the resale market in the USD2,500 range. That said, I would still favour a used GH4 for the superior image quality, excellent MWB and ability to re-use lenses in a future upgrade. The GH4 is also a much more versatile rig for above the water.
Yes indeed, if you take photos. But if you only do video, then I think a dedicated video camera is still superior, continuous auto focus for video is still not quite there yet.
Bill
I used a Sony A6300 with 10-18F4 and Sony 90F2.8 macro in a Nauticam housing for the last 2 trips. Honestly didn't filmed a lot but i think the camera handled the whitebalance quite nice. I always used auto white balance, no filter and filmed in Cine4 - check out the clip below, most parts ambient light
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