I would first establish, based on what long term learning difficulties the student has, exactly what EAA are needed- for example extra time. If a student needs support and uses it, that should determine the need for EAA. So exam access arrangements echo the support already put in place internally.
Then it’s easier to gather evidence: teacher round robin, pupil views.. work samples…
A medical diagnosis from a specialist (such as ASD and ADHD, or an EHCP) means that a form 8 and specialist assessment from a centre approved specialist teacher is not needed, and a senco note/file note must be written. Also evidence collated.
some students , for example those with dyslexic difficulties, (including diagnosis of dyslexia) must be assessed by a centre approved specialist teacher and meet the criteria for the EAA needed. For this a form 8 is needed. (Check which EAA need to be applied for as some are centre delegated).
So in your case the spLD diagnostic reports may be evidence of need /background info on a form 8, but they are not necessary or essential).
What is needed (depending on what EAA you are applying for) is a specialist assessment showing 2 below average scores in 2 different areas of cognitive processing). If you can show the necessary scores you don’t need to gather further evidence of need eg work samples or teacher evidence (new: from this year on).