Buying music previously downloaded via Apple Music

I pay every month for Apple Music. I downloaded about 20 Apple Music tunes mistakenly thinking I owned them and could use them to create a CD for my wife. But I couldn't burn them. Apple Support told me I had to purchase them through iTunes so I did. I found each one in iTunes Store and purchased them. Still it won't let me burn them. The majority of those songs are still identified as being Apple Music selections even though they are shown as "Purchased" in my Music app. How do I clear the Apple Music identity and show them as purchased so I can burn them to disk? I don't want to buy them a second time.