Is there a program out there that can look at these links and download them automatically at a certain time of the day?
It will also need to support overwriting of the existing file in the directory that is user-defined.
You could accomplish the downloading and moving of files with just a few lines of AutoHotkey. You could then create an entry in the Windows Task Scheduler to run it at a certain time. If you want the script wholly self-contained, that can be done, too. However, it will need to run in the background to be able to check what time it is. Small AHK scripts typically take just a few megs of memory so running it in the background shouldn't be an issue.