I had DSA myself ten years ago (IIRC I was about the 3rd centile for processing or working memory, I forget which, but low enough to qualify easily). Since then I have taught a lot of dyslexic students, both those diagnosed at university and those who come up with diagnoses.
A 6 month wait feels like a lot. Better to go up with an assessment in hand. DSA really does make a difference, but IMO what is better is having everyone know that you have a known problem.
Whatever happens, make sure DS is prepared to talk to all his supervisors about dyslexia. In most universities, this should be done for him - either through the disability resource centre or through a personal tutor. But IME even really good systems fail, and it's always worth sending each new supervisor an email explaining the situation. You could probably draft this with him if it's something he finds hard. Just something like
'Dear Dr So-and-so, I wanted to let you know I have been diagnosed as dyslexic, in case you've not been told, and usually use some coping strategies. I have a scribe/use notetaking software/whatever.'
Depending on your DS, he might also want to say what's helpful for the supervisor to do. Obviously this is a bit delicate as some supervisors might feel they were being told how to do their jobs (they shouldn't, really), but if it's something a little unusual, it's worth raising. And with luck, that introductory email will prompt a good supervisor to ask if they can do anything to help, anyway (especially if signed off with a nice 'I'm looking forward to meeting you ...' type bit, which loads of students forget to do!).
That's a bit of a digression from the actual assessment, I know, but IME the assessment is only useful if everyone teaching 1) knows you have it and 2) knows what its recommendations mean! And university teachers mostly aren't trained in reading a report, so may not automatically know how best to teach a dyslexic.