I was able to fix it. Here's what I eventually did:
- Deleted everything that even remotely looked like it belonged to Garage Band: the application, the application support folder, the Garage Band loops in the Library/Audio folder, the software update receipts (both in Library/Reciepts and in /var/db/receipts).
- Restarted the computer.
- Reinstalled Garage Band from the iLife '11 DVD.
- Upgraded to the latest Garage Band using Software Update.
- Open the loops and click to download the additional instruments.
This time, Software update had a "Additional Instruments" upgrade available, and everything seems to have gotten installed.
One warning: Reinstalling Garage Band from the DVD trashed my installation of iPhoto (even though I unchecked iPhoto in the install options). I had to repeat this process with iPhoto (toss the app, reinstall from iLife DVD, upgrade iPhoto in Software Update) before it would work again.