OK, no responses, but for the sake of documentation, in case anyone else runs across it, here is the solution:
I installed JBridge because someone told me it was better with 32-bit plug-ins than BitBridge. But then I got an error saying I needed to run Sonar in Administrator mode for JBridge to work. But running in Administrator mode, for whatever stupid reason, means that Sonar won't recognize mouse buttons that are assigned to keystrokes, even though those mouse buttons work everywhere else. I opened Sonar without using Administrator mode, and the mouse works fine (though JBridge now gives me an error).