Disorganized or Unorganized?

Solution 1:

You could certainly attempt to construct two different usages along the lines you suggest but they would pass most native speakers by.

Consider the very strong case for regarding 'disinterested' and 'uninterested' as having very, and usefully distinct meanings. Some native speakers, myself included, insist on this distinction.

Even in that case the distinction is very frequently not observed, to the extent that modern dictionaries record them as being used as synonyms:

Disinterested is sometimes used to mean not interested, but many people consider this use to be incorrect. Compare uninterested.[Cambridge Dictionary]

If you are disinterested in something, you are not interested in it. Some users of English believe that it is not correct to use disinterested with this meaning.[Collins]

"Some users of English", or even "many people" believing it is incorrect does not stop the rest believing 'disinterested' means the same as 'uninterested'. So if you want to be understood by everyone, you need to be careful.

Likewise if you wanted to use those unorganised and disorganised in the senses you describe you would need to explain that usage before doing so. Otherwise the reader/listener might assume they were synonyms.