Solved my iTunes Match problems on iOS 7

I updated both my iPhone 4S and iPad (3rd gen Retina) to iOS7 on Sept 19. I use iTunes Match, and observed 3 different issues:

1. Some songs on my iPhone wouldn't play
2. Some album artwork on my iPhone wouldn't appear
3. Radio option didn't appear on the iPad

All are solved, so I am sharing what I did. I have an iTunes Match library of about 22,000 songs.

iPhone: I tried turning iTunes Match on an off to no avail. I then set the Music to NOT "Show All Music", and observed that I had several hundred songs loaded in the Music app, some of which were songs that were giving me grief by not playing. Wishing to start fresh, I went to Settings - Usage and looked for the Music app in order to delete all local files. It was not there! This told me that the OS incorrectly thought there was no local music - a database error. But how to delete a database that the system won't acknowledge?

So I went to the iTunes Store and downloaded a previously purchased album. Going back into Settings - Usage, the Music app now appeared, showing the total file size for the newly downloaded album. I deleted all music from the app, and it worked - the Music app was empty. I turned iTunes Match back ON and poof! Everything loaded back in and after a while all my album artwork was back, and all songs played normally, whether locally stored or streamed. Problem solved by finding a way to completely delete the music database and start over.

iPad: No radio, soap. Sorry, I couldn't help that bad joke.

The Music app on the iPad did not have a Radio button. I forced the iPad to restart (hold Home and Screen Lock buttons together for 5 seconds) and when I restarted Music, Radio appeared for a second and then disappeared (!!). I quit Music and restarted it. The Radio button appeared and I quickly hit it, which brought me to the "get started" screen for Radio. Problem solved by repeated restarts (which probably cleared some temp data, allowing the button to appear).

I don't know if either of these will help others, but if so then great!

P.S. - the rest of iOS 7 is working very well on both devices, no complaints worth noting. Nice new stuff.