Maybe I haven't understood the question, but if each member is backing up their own library, wouldn't it be easier for each member to add their name to the file name, e.g. George_Drum_MobileSheets_2025-01-26.msb?
That's how I differentiate between the various instrument library back-ups on my devices e.g. 1st_trombone_2025-1-26.msb, 2nd_trombone_2025-1-26.msb etc.
That's how I differentiate between the various instrument library back-ups on my devices e.g. 1st_trombone_2025-1-26.msb, 2nd_trombone_2025-1-26.msb etc.