How can I move the Class to another Room for Cover?

You can do this quickly; on the Cover Display Screen (via <f5> or <shift-f5>), right-click & choose 'Edit notes or room'.

This asks the Coverer (on his Cover Slip) to take the class to a different Room. 

Note: This is a temporary change. If the room for this lesson has changed permanently, then use 'Make small changes to timetable' instead).

To see the Room on the <f5> Cover Screen, just hover your mouse over the lesson.