The files are being created at a single point in time, daily about 4:00 AM. I'm running my process way after that. I don't have the files open, and in fact I've ensured that I'm able to manually cut & paste them so nothing else is holding them. As far as that line of thought I feel 100% positive it's not that.
Since the time I posted this I've tried all kinds of other things, the most recent being:
1. script task to create a temp directory, copy all the files into the temp dir.
2. foreach file enumerator that goes through TEMP directory instead of 'real' directory
3. script task that renames (moves) them from the real directory to an archive.
Just run into an error every which-way, it seems. Carrying on with my attempts...