The reason I was testing different values in the first place was because {TASK(Active|LastExited|yyyy-MM-dd HH:mm)} didn't work. I see, however, that I had to go get that from the regular Variables because it is not available in the ones listed from the red dot next to the specific field.
{DATEADD(Minutes|{TASK(Active|LastExited|yyyy-MM-dd HH:mm)}|yyyy-MM-dd HH:mm|0|yyyy-MM-dd HH:mm)} and similar constructions seem to work, however. Thanks!
Of course, we ended up getting edit access to the share in question so I could go back to our usual approach of deleting files once we've processed and archived them anyhow, but it's still useful to know how to do this.