Thanks all for your input.
In the end I got a good deal on an EM5 III, and will pick up a Nauticam housing. It's still a lot of money for me, but any other equivalent option was going to be considerably more expensive. I did consider an EM1 II, but the extra size added cost to the housing and it's that little bit less portable when travelling. The EM5 also uses the same battery as my previous E-PL5, so I even have spares of those.
Please let us know how you get on with the Olympus EM III in Nauticam housing/ports - I am looking at upgrading to a 4/3 from my Sony Rx100 Mk4 and the Oly Em5 III is top of my list. Hopefully Olympus lenses start coming down as people sell them and move to other systems.