Sorry for the delay on this. I've had a backlog of work to get done.
So I've updated my Dynamic Renamer script with some new capabilities, one of which includes the ability to call upon external script code to perform actions such as the one you're requesting. This means script code can be written externally and used, and Dynamic Renamer doesn't have to be updated to do small jobs like this.
I've written and tested the script code that does the job you want. It uses side effects in the Rename tool to change the timestamps, and shows you the time stamps as previews in the Preview window's New Name.
There's no reason the Perl script code itself could not be used inside a button and called directly.
Anyway, I don't know if you're still working on this, or are interested in this approach.