Have your tried something like Ecoute on iOS? It's a third party music player and I use it full time since Apple Music was trying show up everywhere in the music.app
Ecoute uses the same library as the default app, shows a nice simple grid or list of your albums/artists/playlists and is well designed. When you use any controls in either app it will be picked up in both. It doesn't matter in which app you start a playlist/play/pause/skip/whatever. With that in mind, using Ecoute as default app was as easy as replacing the icon in the dock. No need for a default music app setting in my opinion.
Ecoute uses the same library as the default app, shows a nice simple grid or list of your albums/artists/playlists and is well designed. When you use any controls in either app it will be picked up in both. It doesn't matter in which app you start a playlist/play/pause/skip/whatever. With that in mind, using Ecoute as default app was as easy as replacing the icon in the dock. No need for a default music app setting in my opinion.
More here: http://www.pixiapps.com/ecouteios/