Audio Files Imported to iTunes Turned into Streaming Audio

I am using iTunes to organize the audio files I am creating with GarageBand and to create my own albums. iTunes Match used to sync these albums to my four Macs without problems.

This worked until I signed up for the AppleMusic trial in addition to iTunes Match.

Suddenly the iTunes Library on three of the four synced Macs was showing quite a few of my own songs as "Apple Music Audio File".

When I create a smart playlist with the rule:

Artist contains Leonie and iCloud Status is Apple Music

I find 17 of my own creations that are all of a sudden Apple Music.

And after the AppleMusic trial ended I could not play them any longer. When I tried, I got the prompt to renew the Apple Music membership.

turingtest2 helped me clone the one good library to my other four Macs and to start over.

This helped for a month or so, but now more and more of my own audio file songs are turning into "Streaming audio" for a change, no longer Apple Music Audio file, with the iCloud status "waiting".

I'm using OS X 10.11.5 on all Macs, with the newest iTunes.

Should I try to restore the iTunes Library again on the three synced Macs from the one good master copy?