K-H, I am at a loss to understand how such a joyful experience for me is not the case with you.
These are the zooms I have tried:
1. Canon EF 28-80 f/3.5-5.6 IV
2. Vivitar Flat Field zoom 90-180 f/4.5
3. Nikkor (AiS) 35-70 f/3.5
4. Nikkor (AiS E series) 75-150 f/3.5
5. Leica 75-200 f/4.5
None of them show any corner softening problems at all. It is remarkable that barring the Vivitar zoom, none are unique.
All behave well.
I also tried a Hoya 80-200 zoom (OM mount) I had with one of my OM bodies (I had never used it before though!) that was down right horrible with weird distortions. I am pretty sure it is down right horrible on its own.
What is the FW number in your NEX-7?