Have you tried DJ with Apple Music? I recently find a method to use Apple Music on rekordbox. That is using a converter called TunesKit Apple Music Converter to convert Apple Music to MP3 and then I can transfer Apple Music to rekordbox. This converter has a free trial version. So you can try it on your own computer.
TunesKit Audio Converter Features
-Support Audible audiobook & iTunes audiobooks
-Convert M4P to MP3, AAC, WAV, FLAC, M4A, M4B
-Retain 100% original quality and ID3 tags
-Convert iTunes songs to MP3, M4B, AAC
-Convert between unprotected audio file formats
Here is how to convert Apple Music to rekordbox:
- Launch this converter and drag the Apple Music songs into it.
- Choose the Format button and choose MP3 for your songs and
- Click the Convert button.