Couple comments...
The Sony and Canon are the only point-and-shoots in your list; the rest are interchangeable lens cameras, in 3 different families. If you want to get an ILC, I'd personally go with the Lumix due to M4/3 lens selection, but I'm biased, I have a lot of M4/3 equipment. But it sounds like you aren't looking for that (?)
You might look into the Panasonic LX100 which has neat retro style controls and does 4K video, not a whole lot cheaper than RX100 mk III though, and a bit hefty.
DPReview has some really good buying guides / roundups, you may want to check their site.
Edit: Also have you looked into EyeFi / other Wifi SD cards?