Another possibility is the observation that SDSF is really scanning/summarizing JES2 datasets. So, is the requirement to store sysout datasets created by batch jobs? if so, then it is possible to code the batch job so that it's sysout is stored.
if the requirement is to store the joblog itself, then get a JES2 manual and read-up on how JES manages joblogs (it has been awhile, so I have forgotten this info.). After learning how JES2 manages its job logs, then there might be an obvious solution to saving them.
The above might have some advantages. For example, what if a new job is added to the system that is needed to be saved? Do you update your REXX code or a dataset of jobnames, or is the JCL for the job itself coded in a way to save the required sysout/joblog?
This makes a difference. If someone has to update a list everytime a new production job is added, then this is time consuming and error prone. If the JCL has to be coded in a specific way then it only has to be documented and it is easy for managers to say "code production jobs in a such-and-so fashion.