It seems a lot of my "greyed out" problems seemed to stem from my not having allowed iTunes to fully sync with my iCloud Music Library. I have a MacBook Pro, so I never leave it on for more than whatever I need it for, which is usually just to do some quick work for my job, or to look something up, pay bills, etc. I think iTunes never got a chance to finish the sync. I left it open for a few hours tonight and all my Beatles tracks seem to be playable now.
Thanks to any and all the advice above, as it all helped me to discover what was happening, and to understand the inner workings of Apple Music a little better.
I'm still running trials of Apple Music, Spotify, and Google Music deciding what to stick with. I absolutely love the suggestions in the For You section, and I feel like Apple Music "gets me", and understands my tastes way more than the others. Apple is the only one for example, that seems to understand that a skate session playlist for an 80s kid could and should have Agent Orange AND Run-DMC together in the same playlist along with the Misfits and LL Cool J.
Spotify is my least favorite, and also seems to be missing the most music, and has no real way for me to add my own non-Spotify tracks to my library. Both Google and Apple let me do this pretty easily. The suggestions and radio are pretty lacking.
Google Music is great to use, quick to get around, great catalog, but the suggestions are barely even there at all. I have absolutely no use for their "waking up in a good mood", "gazing at the stars" , mood-type radio playlists. The radio stations based on a chosen song usually serve up good results though.
I'm totally rooting for Apple Music to get more refined over time. I'm hoping iOS 9 brings some positive changes. I also am really hoping for a web player at some point.