As I had suspected, File History offers a feature to "restore" your files to your PC which will remove the timestamp, whereas copying and pasting your files from an external leaves the timestamp intact. There is absolutely no need for a complicated script or anything like that.
When I restored my computer to factory settings awhile back, I changed the name of my machine to something new, and I had since started a new File History for the restored machine's files -- in other words, I have two backups, which initially seemed to prevent me from using both, as the File History main screen only presented me with one option -- the current computer's File History.
However, this was not a problem when I found that you can visit File History to restore files from a previous backup as a feature.
- Go to Control Panel
- Under "System and Security," click "Save Backup Copies of your Files with File History"
- Click "Select Drive" on the left
- Choose the external drive. In my case, I had both backups on the same external.
- When you click your drive, the "Select an existing backup" window appears.
I selected my old computer's file history, located the files on which I was sick of having timestamps, and restored to a new folder on my Desktop. Now Audacity recognizes my projects again! No harm done.