Hi Avenarius,
Sorry to hear you haven't got past Stage 1 this time. Somewhere in amongst this 87 pages of interview goodness I seem to remember seeing that NATS have (in the past) given feedback on why candidates have failed Stage 1 - it appears they can give you some idea of which parts you did well/not so well in. Perhaps that's a more productive and useful thing to do rather than try and convince them that they should see you? Personally I think anyone willing to ask for feedback or constructive criticism should be well-thought of - at least you care enough to try and improve and show them what you can do next time round.
Out of interest (since I'm still waiting on S1 results myself), how long did it take until you heard that you were invited to do the personality test?