I think it is a good idea to keep each cover art file in its respective album directory, side-by-side with the music files themselves (as well as storing the cover art in the music file as a tag). That is how I do it, for a variety of reasons, and it is a common practice. If I understand correctly, that is how they are stored on your backup drive right now.
If so, and assuming the overall music folder structures are the same on the two drives, then it is extremely easy to copy the cover art files from the back up drive to the new music drive, preserving side-by-side locations. Simply use a file/folder compare utility, such as Beyond Compare. Compare the two top level music directories, including all subdirectories, and then copy the "missing files" from back up to current music folders, which can be done in one fell swoop by the utility. BTW, investing in a good file/folder compare utility is a great way to independently confirm file synchronization between your primary storage disc and backup discs.
MC has a setting for this organization scheme: Options > File Location > Cover Art > Audio mode > In the same folder as the file.