I know I can change the path for saved files. But, is there a way to clear the “backup” path, and have the file saved to the same directory it’s previous version is saved in?
Open a LO application. In the menu click Tools > Options, in the dialog that opens, under LibreOffice, click on Paths. In the right hand pane click on Backups and then press button Edit… to change it. You can’t change each time you save though.
Instead of doing the above, File > Save a Copy allows you to manually save a version (I would suggest adding date (YYYMMDD) to end of name), but carry on working in your original file.
There is an extension to do the above automatically. It looks older but might still work, see timestamp-backup
Cheers, Al