Well, I'm going to declare victory here, and hope I don't have to eat my words. Blackberry tech support at 877-255-2377 took 45 minutes to get me to a tech, but he solved it.
I don't know whether this part matters, but for the record: before calling tech support I followed the directions in Apple's "Advanced troubleshooting" guide to sync services -- http://support.apple.com/kb/TS2481.
I tried a sync again and it froze, so I had to force-quit BB Desktop.
I backed up the Mac Address Book and iCal. I backed up the Blackberry. The biggest problem was my calendar. It had not been working both ways for a while, so only the Blackberry calendar was up to date. I deleted all calendars on iCal, then created a new blank calendar.
Then I called Blackberry support. The guy told me to go to the Device menu on BB Desktop, choose "Forget Device," and repeat until all devices were gone.
Then, with Blackberry Desktop still running, I plugged in the Blackberry. I told it to sync two-way, all events, and default calendar for new device entries was the new, empty iCal calendar I had created. The first sync took maybe 45 minutes with a few thousand calendar events, but it worked. Changes on either side now propagate properly.
I had a couple of false starts, and the first sync on my computer takes a LONG time. So I commend Blackberry support for staying with me. He twice said he would call back in half an hour to check progress, and both times he did it.