Remapping my music and video folders

If the names match (which they should as you got them from the recycle bin), it should work.
Whats wrong with reinstalling though? If you're worried about your settings - they will all be preserved except for the autorun file.

Where did you install the Platform to? The root of a drive (e.g. X:\ with PortableApps in X:\PortableApps\AppNamePortable folders), or a subfolder (e.g. X:\SubFolder\ with PortableApps in X:\SubFolder\PortableApps\AppNamePortable folders)

The Documents folder should be in the folder that you installed to Platform to (X:\Documents if installed to the root of the drive, X:\SubFolder\Documents if installed to X:\SubFolder\), and the Music and Videos folders should be in the Documents folder (Note: newer versions of the Platform use a "Videos" folder while older versions use the "Video" folder)

Hope that's helpful.

Also as Simeon said, installing the Platform over your current install will not harm your settings, it will rebuild the folder structure (placing the Documents, Music and Videos folders in their proper places), and it will replace the Autorun.inf file in the folder you installed to (preferably the drive's root) which (if installed to the drive's root) will reset the label of the drive to "PortableApps.com", but that's easy to change again if you want to.