Hi Swandy,
After our last exchange I played around some more. One thing I noticed is that iPhones and iPads act differently with these issues.
FIrst, I was able to listen to synced from iTunes content in airplane mode on my iPad Air2 just as I have been able to do since I bought it. Enabling Apple Music makes no difference. It still works. However this iPad has absolutely no purchased content. When I say purchased I mean either content from the iTunes app on the device, paid for with my credit card associated with my appleid or "free" content that I saved by downloading via Apple Music. I have not had any issues with my content disappearing like others have. I have never set up iCloud music on this device or on a computer. If I am streaming and want to save something on this iPad I get an error saying I must turn on iCloud music in settings.
So we have basically the same experience.
My husband's iPhone 6 he has never enabled Apple Music. He can play anything we synced to that device from his personal itl file on my computer. This is via cellular when out of the house or via wifi at home and in airplane mode. He also does not purchase music from the iTunes Store. He uses our ripped music.
My iPhone is another animal. I am going to connect it to iTunes and remove the 20 or so synced albums on it and sync to it a half dozen or so free Starbucks tracks which I hate and could care less if they disappear forever. Then I am going to download some Apple Music content and try again.
With all that said however, I think it was the abrupt cutting off of cellular signal while streaming that upset the app. When you listened to your music you had downloaded you still had cell coverage. When I tried to do it I had no cell coverage. Nor did I have wifi out in the middle of nowhere. We have established that a cellular connection must exist for downloaded content to play, necessitated by Apple needing to verify an active subscription. I am not able to replicate the exact circumstances of no signal while at home. But I think I know what happened. I had Apple Music on. I had iCloud music on. The cellular connection was abruptly terminated as a result of driving out of coverage. The app, to use the vernacular here, freaked out and refused to do anything at all, including playing synced content. My music was all still there, it just was not accessible, because the app totally crashed. I checked the error logs and I could not make heads or tails of most of it but it was clear the app crashed dozens of times in rapid succession.
I do have one question and that is that you said you downloaded all those tracks through iCloud music library. How did they get there in the first place? Is this music you saved to your device by using the plus sign next to the album track or playlist name, or did you do this via a computer?