The Sony kit lens has some sweet spots (around 40mm @ F5.6 it's not half bad, for example) but huge distortion problems at 16mm. Works fine with the CMC at the longer range, though. Never had problems with AF speed of the Zeiss 12mm on my NEX-6 - would be surprised if A6300 is slower than the NEX-6. Great lens. Macro on the Sony is a problem. I used a 100mm Canon lens at the time, MF only. I have not seen a single Sony camera (including my 7R2) that focuses the 90mm G Macro "fast", so I'd be surprised if this was something the A6300 could overcome - one of the reasons why I went to DSLR, to have useful AF speed with high quality macro lenses.
Flash sync speed is an issue. I used Nikonos adapters on my NEX-6 and shot the strobes in manual, works perfectly. Wanted to have a TTL strobe trigger built, but housing (Nauticam) was too small for that.
Even the housing for a APS-C DLSR is substantially bigger than the housing of a mirrorless (talking alu housings here). At the end of the day though, it does not really matter - what "kills" you are the arms and strobes and focus lights, so even with a smaller housing, you will end up with a system almost the same size. I've met people who had RX100 rigs larger than my DSLR setup.
From what I've seen - never used one, but dived with a number of people who knew how to use their Olympus - the Olympus ecosystem has a MUCH better native lens selection than Sony for underwater use. Smaller sensor, though, and I always preferred the colour rendering of the Sony - YMMV.