I take it the tribunal was for refusal to assess?
If your appeal is upheld the LA must seek advice from
"a) the child's parents or the young person;
b) educational advice (usually from the head teacher or principal);
c) medical advice and information from a health care professional;
d) psychological advice and information from an educational psychologist;
e) advice and information in relation to social care;
f) advice and information from any other person the local authority thinks appropriate;
g) where the child or young person is in or beyond year 9, advice and information in relation to provision to assist the child or young person in preparation for adulthood and independent living; and
h) advice and information from any person the child's parent or young person reasonably requests that the local authority seek advice from."
SEN regs 6(1)
H can include OT, SALT and a psychiatrist &/or CP. In this case I wouldn't hire a teacher to assess, nor an independent EP at this stage. Wait to see if you need to appeal refusal to issue or BFI and then target the assessments you need most.
If your appeal is not upheld is your aim to gather evidence then reapply for an EHCNA? If so, I would go straight to an independent EP rather than hire a teacher.
For SENDIST I would just get independent reports from OT, SALT, EP and/or psychiatrist &/or CP, they are far more detailed, specific and quantified than LA/NHS reports and SENDIST will consider them. It is often reports that win tribunals. If you are eligible for legal aid it can cover the cost of assessments for tribunal. 'Parents in need' can sometimes help fund assessments, too.
Have you looked at IPSEA and SOSSEN's websites? They both have helplines as well.
NC levels don't officially exist any more. Submitting a SAR to the school may help you gather evidence - both of DD's psychological state and of her academic levels.
Also, you could ask MN to move this to the SN boards, there's some knowledgeable posters who can help with tribunals.