You can change the library field value without removing the physical image files from the file tags if you make the music files temporally offline:
1. Change the base folder name outside MC, start MC, select the music files and do: right-click > Image > Remove Cover Art. Close MC --This will clear the "Inside File" values from the library data.
2. Change the base folder name back, start MC, select the music files and do: right-click > image > Quick Find In File / Cover Art Directory --This will find the Folder.jpg files and add the external links.
However, this is not going to make the directory path appear in the exported XML file. MC uses cleverly only the plain file name in case the image is besides the audio file. This is good because when file folders are moved the image file links remain correct. (MC does not have a mechanism for changing the links automatically.)
EDIT
MC seems to ignore my request to collect and place folder.jpgs in relevent folders - and relies on tag images.
Do you already have the Folder.jpg files in the file folders? MC cannot automatically extract the image files from the file tags.