There is indeed a hidden folder in the MODS folder that contains the backup files. And guess what it's name is.
My guess is your game file structure is corrupted now. Instead of trying to find the modded files and getting them replaced with the originals you might aswel start thinking of a re-install. I remember older versions of JSGME had a bug that could mess up the file structure in certain circumstances. Make sure you have the last version for your next install.