The issue with the App not being allowed to play songs from Apple Music subscription still exists... because frankly it is all in the hands of Apple. I would love to resolve it as it is the majority of the complaints and support requests for the app. As soon as Apple makes it an option, I will have an update to support it within days.
All songs you purchase from iTunes should work. If you are having issues with that, I would recommend disabling the 'Show Apple Music' in the Music section of the iOS Settings applet. Then for songs that don't work, delete the local copy and redownload from the cloud.
I do understand your impression that 'Apple Music' songs should work with the app... I'm right there with you. But I do mention directly in the app description that they do not to try to avoid hassle for people.
I have found an option that works to avoid having to buy songs you already have from Apple Music. On a MAC or PC, Download a free trial of this application:
http://www.macsome.com/itunes-converter-mac/That application will convert Apple Music subscription files to non-restricted mp3 files that you can then email to yourself and import to the app.
The only restriction on the trial version of that converter application is that it cuts the conversion at 3 minutes, but that is usually plenty of time to get the part of the song you need for the walkout.
If you still have no use for the app, feel free to request a refund from Apple, but please let them know that the reason is because they won't allow third party DJ style applications to play songs from your Apple Music subscription.