I have known one university request from a candidate that they paid to have their written scripts typed, while they dictated, at the point it was decided the assessor was unable to read the writing. It was not exactly terrible, but small and cramped. However, that was a long time ago when it was much less usual to have accommodation for typing by any candidate, so decided after there were a lot of scripts submitted that turned out to be 'unreadable'.
It would be worth thinking through whether this could be an offer to suggest, or to pay a scribe for the exams if the university can find you one. They may not accept this, as they would almost always need evidence to put reasonable adjustments in place in advance. But it would then mean that you have the right amount of time - i.e. as much as you need - to get proper advice and assessment ready for the most important exams.
There is one more thing to be aware of. It depends on university systems, and it varies, but it's worth bearing in mind. With some learning differences or health conditions, declaring them to one area of a university does not mean that they are automatically shared to all of them and translated into an adjustment - so it is a very good idea to ensure that all departments that will need to be aware are contacted directly (e.g. the exams office) to make sure it is all consistent. This is, again, partly due to GDPR expectations and the systems they have to fit with.
Examples can be that some will declare a health condition on enrolling, right at the start of their courses, but that this data is not necessarily transferred through Student Support and on to the Exams officers. If someone moves course or university, even if records are transferred, this other personal information very rarely is. Better to ensure that you have flagged it up, when there is a decision on specific support in exam conditions.