Oleg’s comment made me think that I might be able to find a plugin that would allow me to edit the .htaccess file.
I installed the WP htaccess editor plugin. and was able to edit the .htaccess file despite not having shell or ftp access to the file system. I insterted the following line at the beginning of the htaccess file:
RedirectMatch 301 ^/events/[0-9]{4}-[0-9]{2}-[0-9]{2}/$ http://example.com/events/upcoming/
Now my pages are redirecting properly instead of showing 404 status.