Save all Apple Music content for offline use

I'm loving Apple Music, but it ***** there's no button that just lets you save it all for offline use.

So I created a playlist, added all my music (music that's available to be uploaded) to a playlist, and tapped "Make Available Offline." There's about 2200 songs.. and it starts downloading okay... but then will drop to about 200 songs downloading, and a lot of "Looks like this isn't here anymore.." appears. Can someone help please? I just want to save my music!

I've even reset my phone from a fresh installation.

Thanks guys.