You are at a very good (and bad) time for upgrading. First reaction - Wait for the new camera reviews in 2017 and the AX100 replacement and decide then.
An external recorder for your current camera I don't see giving you any extra image quality it will still be 8bit and 4:2:0 - although uncompressed - its still has a lot of data stripped from the sensor. So unless you fancy a super nice viewfinder - It wont be worth it.
The 'first' generation of consumer 4K cameras with 4K@30p are now 2yrs old (GH4 and AX100 as an example) and the current mid tier models (GX8, A6300) are not really setting the world on fire with hardly any improvements (well apart from the A6300 when it overheats!)
So obtaining one of these first 4K cameras, you could get a bit of a bargain and still have a great improvement in image quality - IF you can get one for a bargain.
The Sony A7 Mk II's are interesting - with their amazing low light and also fast phase detection AF. Alas the limited lens choices for me don't sit well. Plus they are not cheap and you know Sony will have the Mk III's out for Christmas!
Its odd at the moment, that we are caught with DSLR type cameras having massively better image quality than camcorders (DVX200 not much better than the GH4 (and no housing), the Canon's/JVC suck at 1080 etc - and that was (at the time) the reason I went down the GHx road (there was no AX100 at the time, when I got my GH3 and housing) and the semi-pro Sonys of the FS5 and FS7 are serious money once you get the firmware upgrades and Sealux housings...
The BlackMagic camera really want a controlled, well lit environment to shine - and when I looked at the BMPCC, it was awful to use in a housing, the amount of hours in front of a PC to convert the RAW stuff - just didn't seem worth it add the fact its a S16 sized sensor so needs super wide lenses to get even a 'normal' wide shot. Everything says no to me.
The AX100 would be a serious contender for me, if I had nothing and needing something 'today'. Pete in Oz has worked out that the Magenta filter fixes a lot of the WB issues and it benefits from all the camcorder features (parfocal lens, OIS, continuous AF that doesn't hunt, ND filters and then you have the video centric options on the housings like the flipable internal filters and excellent buoyancy characteristics) - so a really good choice. It is sadly let down by the awful rolling shutter thou - but others can comment if this has any effect underwater.
If I had nothing and could wait, we have info on the 'new' models coming in 2017 and they are coming with 4k@60p and this along with HDR will be big - very big, as you know the camera aspect of an underwater camera 'rig' is just chump change once you buy housings, trays, lights arms etc - and investing in a 2yr $1000 camera (plus the $3000+ on housing) now doesn't make sense, now we know what is coming.
Need today: AX100 or a knocked down GH4.
Wait for 2017: GH5 or AX100 MkII (whatever they call it)
Im happy with my GH4 and Atomos Flame - its missing a lot of video features - but I've learned to work around them (rubbish AF, no AutoISO in Manual mode etc) - but the image quality I'm super happy with and if the rumours of IBIS are in the GH5 and if they improve the AF, i'll be happy to stay with the GHx series worts and all. (But always with a casting eye on the Reds and FS7