"cannot play my own music in apple music: I've got a monthly subscription to Apple Music, primarily for the simplicity of having my music sync'd across my devices (iPad, Mac Mini 2 Pro, iPhone, Air) without plugging everything into the main storage on my Mac Mini.[...]"
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Are these MP3 files?
If these are not MP3 files, but rather m4a files, then they are(or have become) Apple purchase format. So, contact Apple Support, and perform a screensharing session with them, asking them why this is occurring. Being home music (not purchases from the Apple Store), this should not occur. Go here, and select your country: Contact Apple Support - Apple Support
Notes on Playing Apple Music:
A. Authorize this Device:
If this is associated to your Apple Account, then you need to authorize ti to play it. Note how it says that "you may authorize up to 5 computers to each account." Go here: Authorize or Deauthorize your Computer for Apple Account Purchases - Apple Support
B. Use Family Sharing:
Is this purchased with a different Apple Account? If so, you need to run it through that. So, set up and use Family Sharing to access thing between Apple Accounts. Go here: Set up Family Sharing - Apple Support
C. Verify this was Purchase with this Account:
Log in here, and make sure that this was purchase with this account: View your Purchase History for the App Store and Other Apple Media Services - Apple Support
