I tried out the A7 and I think it's absolutely phenomenal. The biggest issue I had with it is by far the battery life during video being pretty weak - something the GH3 doesn't exactly have a great strength in either (or most non-camcorders, to be honest) I don't know what moire or aliasing POV saw if he's used it, but I certainly didn't see much if any in the stuff I shot with it...
the sensor and image quality is great, and the codec is totally fine. I've used it a bunch recently.
I used it with all canon FD glass. 28 f2.8, 50 f1.4, and a 100 f2.8. Worked perfectly.
The one thing I didn't test is the stereo input, and how it takes in sound. I personally record all my sound using a Field recorder rather than an external microphone, so I cant tell you how well it did. I'd assume just as well as the GH3, though.
...all this said, for the price you'd pay - and if you're doing just video, and if you're not doing just cinema style shit, i'd totally skip full frame, and go with something like a VG20 or VG30 and buy a bunch of really excellent old Minolta/Canon FD glass. Full frame format is totally unnecessary for shooting skiing and sports. Plus, then you get an on-board microphone that's actually pretty good (records in dolby 5.1, too). And yes, the 1080/60p you're looking for.
/gearrant