As it always possible with CTSA, you can use few approaches, depends on your implementation and maintenance needs. Such as:
1. if batchrun command issued by cronjob cause for transaction creation, you get transaction number in batchrun output, and then can update field remarks in the same transaction record with neccessary information.
2. it seems you currently execute batchrun in your scripts in ESS owner security context (using -A option). You can extend it using option -N <any_ess_admin> and create for such needs different ESS admins (say - having its ESS login name as cronjob script name). Moreover - you can permissions of those admins by access rules so they will be limited for only relevant tasks.
3. you can use site_table in ESS repository or some non-ESS table to register all details for such actions from the same script...
Hope one or combination from above can help...