Our reasons are that RMGS is a mixed school which is better suited to DS
You would need to establish why this is important.
their specialisms seem to be (although not terribly clear on their website), maths & science, which are DS' favourite & strongest subjects.
This would be all right with supporting evidence (letter from class teacher, school report). Worth ringing the school to check their specialisms?
it's the closest grammar school in terms of actual travel time, only by minutes & by train not by bus, so more expensive.
"Closest grammar school" is worth a brief mention.
Is the fact that DS would prefer a mixed gender school even worth a mention?
I doubt it - unless you can show why it really matters. Your reasons, as a whole, have to be substantial enough to outweigh the prejudice to the school!
And also is the fact that the specialisms are well suited, anywhere near a strong enough case for appeal?
It is worth including in your case if backed up with evidence.
DS is first on the waiting list for this school at present, is this worth mentioning, as the school has score as one of the main criteria for admissions?
Panels are not
allowed to take account of where someone is on the waiting list. No reason why you shouldn't mention his good score, though.
Also I thought that somewhere on this journey, I read that NVR was related to science ability, is this true & would it be worth mentioning strong scores on Maths & NVR, for our case?
Yes, if you're right about the school's specialisms.
Hope this helps.