I was looking for a plugin that John Beardsworth created for this purpose, but couldn't find it.
Anyhow what you want to do is right-click on the top most folder and click on the 'Show Missing Photos' button, not Synchronize. I would then open LR and Explorer or Finder windowed side-by-side and try to determine the new folder location by right clicking on the first image in LR and selecting 'Go to Folder in Library' and then reassociate at the folder level. You can use Explorer or Finder search to locate the "new" folder location by searching on the file name. Proceed this way down the "missing images" displayed when clicking 'Show Missing Photos' at the folder level. At some point only images orphaned by "partial moves" from one folder to another will be left. These you will have to reassociate one-by-one.
Take your time – As long as you do all of this inside LR you will NOT lose your current reorganized folder structure. Sorry for any confusion.