I've replaced the stock music app w/an app called Melodies (
https://itunes.apple.com/us/app/melodies-google-music-client/id492178411?mt=8 )
It works very well for me, and offline listening is great.
Now I only have my favorite songs for offline, but I can still listen to some other ones online when I want without having them take up space. Kinda runs up my usage however, but I mostly listen to offline songs.
I tried the app you mentioned and didn't like it, so i'd definitely suggest Melodies for a Google Music client
EDIT: I linked the free version, but I use the paid version which is significantly better and I'd suggest getting it, I think it's like $2.
EDIT2: The free version doesn't support offline it seems, but the paid version is actually only $.99 so yeah.