Fix "Cloud Status: Waiting" for songs in Apple Music

I have all my songs on an old iPhone.

I have purchased Apple Music, to sync those songs over to a new iPhone

So far, so good.

But:

In "Apple Music" and the music App on my new iPhone, various songs are not available. On the Mac, they show "Cloud Status: Waiting". (About 1/3 of my music library - over 5,500 songs)

It is completely random. For instance, on the album "Birds of Fire", the title track is "Waiting", but about half of the other tracks are fine.

Is there any way to fix this?

Apple Music is not impressing me so far! :-(