I remember you well from last year, as we were both in the same boat. I am so sorry to hear you've a similar story again. You know, the more I think about it, and the more stories I hear, the more that I have come to realise that NVR is such a complete irrelevance.
I'm sure you remember our story from last year (strikingly similar to yours) and we put my son into the private sector too, having passed the independent exam, and likewise he is flying there - infact he's just been asked to take part in a maths competition. As I'm sure you also remember, he did amazingly well in his SAT's, placing him in the top 11% of boys for the county. My eldest son only scraped the NVR when he did it, so he did get to the Grammar, and he consistently performs at the top of his year, coming 2nd in the year in the year end maths exam in July.
It's interesting to note that Kent are working on cumulative scores, rather than individual this year, which makes me think they are (finally!) beginning to understand the complete nonsense of the supposed significance of NVR.
I think that NVR tests 'suit' some children and not others - but the theory that it tests 'innate intelligence' is fundamentally flawed in my opinion. I appreciate my opinion is probably worth diddly-squat in the world of educationalists, but when what you see in practice so often seems to negate the theory, you really have to wonder.
Good luck again for your journey this year, and I feel for you that you have to face it once more - it's truly exhausting and stressful. Sorry, none of this answers your original question - it would be great if you could find some research - I tried last year to find something about the relevance of NVR to achievement, and I did find that it was far less correlated to achievement than verbal reasoning was. However, I didn't bring this up in the appeal, as it felt like I was criticising the system (never!)
Once again, all the best, and I really hope for a positive outcome x