Truth to tell I'm not really sure I quite understand the backup process you're undertaking, but let me "throw out" the following for your consideration...
1. From what I can gather from your description of your backup process you are working with ten different USB external enclosures, each one containing a 2.5" HDD (SSD?) and each one of those USB external disks containing different backup data from each other.
2. For some reason you have a need to coordinate the backup data on each of those ten USB external disks with a specific internally-connected HDD that contains the original data.
3. I would assume from this that the original music files are categorized according to the type of music contained on those files, e.g., jazz, folk, classical, etc. So that you desire to maintain both your original files + backups in that categorized fashion. Or perhaps the music files are categorized by era or some other fashion.
4. Although you have stated the number of disks (10) comprising the total backup of the music files you have not indicated the total volume of data involved. Is it reasonable for me to assume the total data is not more than 6 TB? Perhaps considerably less?
5. Assuming that's the case, would it not be practical to utilize a single USB external enclosure containing a 6 TB HDD, multi-partition the external disk so that it contains ten partitions (perhaps of different disk-space capacity) and accomplish the backup process by cloning the contents of each of the ten internal drives to a specified partition on that USBEHD?
6. I do note your present ten USB external devices contain 2.5" HDDs, however I'm assuming for backup purposes the 3.5" HDD (6 TB disk, for example) would be more practical.