A few minutes instead of seconds would've probably made it worse for the passengers... unless they didn't notice it because of the storm, as you said. But I doubt that. Aircraft engines impart it a very noticeable vibration and characteristic sound.The written article cites a radar site as indicating that they dropped 13,000 ft (but no indication about the amount of time it took). I can easily believe that they dropped that much altitude while going for the restart, but it happened over a few minutes (two to four, probably), not a few seconds.