NEX 6? Any downsides?

The GX-1 does not meet your criteria any better than the Olympus you already ruled out as it lacks a viewfinder.

Before you get the NEX compare the size of such a large sensor kit and consider how few lenses it has.  The m4/3 has bodies with flash and viewfinder whcih would result in a smaller kit.

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See my plan (in my profile) for what I shoot with. See my gallery for images I find amusing.