Basil,
I'm not going to get into the technical aspect of the sensor size vs depth of field. Intercepter121 is more into that kind of stuffs.
As for Octopus picture, keep in mind this is a screen grab of a 30fps video. When playing back the video, you won't see any of the noise at all as the rock/sand kind of muddle everything together. I didn't try the "4K Photo" feature so I'm not sure what's the result of that.
I have both the GH4 and the LX100. The feature on the LX100 is just the same as the GH4 except that you have external HDMI and sound recording on the GH4. I used the GH4 for land, and actually test dive with it when I was renting the housing for it. The GH4 housing is very big, and keep in mind, the lens on the LX100 is equivalent to the Panasonic 12-35mm F2.8 lens, which cost about $800, then the port etc. The port for the Panasonic 12-35mm doesn't allow you to screw on diopter so it's less flexible, and expensive! Trust me, I was very close to pull the plug for the GH4 housing.
If you were to get a new set up right now, 4K is the way to go unless you change set up every 2 years or so. The size of the LX100 is very manageable, I tried to use tripod underwater but because some creature move so fast, moving a tripod won't work, I mean, have you seen a "Pikachu Nudibranch"? That thing move fast for a nudibranch!. With the LX100, I'm able to start and stop recording with one hand.
Yes you're right, 4K downsampling would get rid of most noise, it's call "Noise averaging". Beside this advantage, you can record in 4K, stabilize the footage and output to 2.7K or 1080. the 2.7K will look great on any Thunderbolt monitor. Since 4K is 4x the resolution of 1080p, you can also crop in to "magnify" your subject when you output to 1080p. For example, I came across "Sheep nudibranch", these creature are like 2mm, 5mm max. My dive buddy shot with the Canon 5DMark3 with 100mm macro lens and a Nauticam SMC, let's just say his doesn't turn out well. I shot with the LX100 with the Nauticam CMC-1 with a +7 diopter stacked on top. It looks quite small, but once crop to 1080p, it's a good size to see the detail, you just can't crop in to fill the frame with the face of the sheep nudibranch.
Here is a screen grab of a video of the nudibranch, it was shot at ISO320. By shooting 4K, you can actually see the texture of the body, which is like a frosted glass.

Since you're interested in photo, I tried to shoot photos in 2 dives, and gave up because I wanted to focus on video and it was the reason I bought this camera in the first place instead of the Sony RX100 series. I have a Sea & Sea YS-D1 and these are the result I got, the jpg is straight out of the camera. You can judge the depth of field, sharpness (the Lens on the LX100 is high quality lens).

For the hairy crap, I have my +7 diopter on, and it's causing a bit of chromatic aberration:

PS: Please don't use goPro as your primary video camera, I'm going to leave it that way since I don't have good thing to say about it.