Alternatives to Apple Music for people who own their own music

Anyone have any solid recommendations for a great app that can manage a large music library of owned music files and sync these songs to my iPhone?

I've used Apple Music (and formerly iTunes) for a very long time and like to actually own music as well as stream it, but increasingly it seems Apple Music isn't designed for people like me. If like me you buy songs from Bandcamp AND want to stream other music through Apple Music, the app doesn't work correctly on my Macbook or iPhone. The "Sync Library" feature prevents me from syncing Bandcamp songs to my phone but without it, the Apple Music subscription is pointless. I've got a lot of value out of Apple products over the years but the world will always be bigger than Apple. While I'd like to use Apple Music alongside other music sources, it's clear Apple doesn't want that, so it's time for me to find an alternative. Anyone else had this problem?