I had my collection sorted a little similar to your system for separating into rock , folk and jazz , while I was sorting my classical selections by conductor then by composer since they were all were all conducting the Chicago Symphony .
First I rearranged the classical , first by composer then by conductor then I tackled the big job rock , folk and jazz . I use the alphabet minus the word The , so Beatles, George H. by the Great Society and Grateful Dead , John L between John Cougar and John Mayall . and Paul M by Pink Floyd . Where to put Rod Stewart ? with Blind Faith ? Faces ? no under R . Dave Mason = D , Traffic = T . This way I don't have to remember which group somebody was in . Do you have Led Zeppelin with the Yardbirds ? or Jeff Beck or Eric Clapton with them also ? kind of confusing .
At least it's one way to think about it .