Dave,
If you get the job ask them to place the chairs on the tables at the end of service and check that they will replace the furniture the next morning. Most places will agree to this without a problem. With that agreed you can start at the furthest point, clean a section and then place furniture on it. As you complete more sections in this way you will end up with one large section with no need to move more furniture, which will speed things up no end.
Simon