After some additional searching (new search terms inspired by gbn's answer and u07ch's comment on KMike's answer) I found this, which completed successfully in 2 seconds:
ALTER DATABASE <dbname> SET OFFLINE WITH ROLLBACK IMMEDIATE
When this still fails with the following error, you can fix it as inspired by this blog post:
ALTER DATABASE failed because a lock could not be placed on database 'dbname' Try again later.
you can run the following command to find out who is keeping a lock on your database:
And use whatever
SPID you find in the following command:
Then run the
ALTER DATABASE command again. It should now work.