Upload & Sell: Off
Don't assume the D600+Zoom will have better AF than the NEX-7 and LA-EA2, AF performance should be comparable overall and the NEX/LA-EA2 whould be faster on the centre point.
I'd take the 16-50 over the 16-80, it's better optically and mechanically, only marginally heavier and AF's faster and quieter. You give up a little reach, but that's just a good reason to track down a cheap 85/2.8 SAM to cover the difference.
I've done some event work with the NEX-7, 16-50 and LA-EA1 (so slow AF or MF) with few issues. I rather miss that lens (sold it over the summer during a significant cash pinch, just waiting to see what the Zeiss E mount zoom is before deciding on re-acquisition as I'd like to avoid DT lenses as much as possible and keep my A mount investment full-frame).