Workaround: I wish there was one
You could write a VBScript or batch file that copies your latest back up copy to a specified folder that does not have this attached date. Windows TaskManager can be set up to perform this script a safe interval after your server scheduled back up takes place. Then your back up software can do it's thing with this folder.
A bit of a pain to set up, but workable. I use a similar VBScript to copy most recent nightly back ups to a different machine on my network.
Thank you for your post (and thank you PhilModJunk for the workaround).
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