Hmm...let's see if something like this would work.
1) If I were using FTP Voyager Scheduler, try to create six identical Site Profiles, but each one would provide a unique auto-rename rule.
2) Then, configure six tasks where each one points to another Site Profile that you created in #1.
3) You can then set each task to run at different times throughout the day. This would essentially create six files at the end of the day after each task has executed.