I was told by Support to re-download the installer from the website and run it. I did - first it uninstalled the current installation and then re-installed a fresh copy. It locked up during the first re-install - after 60 minutes of being hung I force quit the installer and tried it again. It successfully installed Studio. The fresh installation does not crash when AI Clear is invoked, so it works now. Not impressed at the need for brute forcing the process.
Bottom line - if it doesn't work, reinstall Studio. I have no idea if an update was added to the application to address whatever issue was causing the crash, but at least it works now.
Thanks AI Don for your replies.