Before you set the database to SINGLE_USER, verify the AUTO_UPDATE_STATISTICS_ASYNC option is set to OFF. When set to ON, the background thread used to update statistics takes a connection against the database, and you will be unable to access the database in single-user mode.
I got to know this only after the fact. What do I do now, when shutting down the entire instance is not an option as there are critical DB's on it as well?
I don't have the permission to kill the 'sa' login TASK MANAGER processes that the statistics update seems to use, and even having tried a brute-force trick where I'd just try to get into the DB some 3000 times in a row for a few times, doesn't help.
Even though I have the VIEW SERVER STATE permissions I can see no stats jobs by querying sys.dm_exec_background_job_queue so KILL STATS JOB doesn't appear to help.
Any advice is appreciated, thanks.