You desire to preserve the original sleeves in probably more trouble than it is worth. You'll need to not only clean the sleeves for aesthetic reasons but also decontaminate and kill all the mold/mildew spores. Otherwise, the whole process starts over, especially if humidity rises above 50%. See the attached link for a discussion of the conservation issues related to your problem. While the link discusses books, not record jackets, the problems are the same.
https://www.library.cornell.edu/preservation/librarypreservation/mee/management/mold.html
https://www.library.cornell.edu/preservation/librarypreservation/mee/management/mold.html