I wanted to downgrade back to version 7.6.2, but it wasn't as easy as just copying the app from my PowerBook to my main Mac. Then I had the idea that it's possibly a matter of the ID3 tag version. When you select a track and open the track info, you can see the version of the ID3 tag. For me, most of my tracks had an ID3 Tag v2.2.
I selected all tracks and converted the ID3 tag (via the Advanced » Convert ID3 Tags menu item) to the latest version (2.4), and that did the trick! Now playing a title with umlauts doesn't damage the ID3 tag. I don't know what Apple did that causes iTunes to have a problem with umlauts -- nor do I know if I'll have to convert the ID3 tag version for all new tracks I import -- but maybe there's a bug fix in the near future. Until/unless this bug fix is released, though, I can now use iTunes as I'm used to.

