What if you change the order of the process?
1. Create a copy of the folder for reference.
2. Replace the data supporting files on the original folder.
3. Open the TWB file. It will still point to the original folder but because the files have been replaced, the workbook will reflect any changes on the data.
The older copies of the TWB will be pointing to the wrong folder now (the original folder) but since the data supporting files are part of the copied folder, if you ever need to go back to a prior version, you can update the connection. This would make sense if it's less common to go back to an older copy that generating the new copy which sounds like it happens every month.
I'd also encourage you to up-vote this idea, which mentions a few workarounds too: https://community.tableau.com/ideas/4167
Hope that helps!
Thanks Santiago for the suggestions and the link. I definitely upvoted the suggestion about having the configuration option of choosing Relative v Absolute paths. I work with too many workbooks that reconnecting datasheets every new reporting cycle is extremely cumbersome. I hope Tableau adds this in future updates.