RX100 - difficult shot, long table of people - How would you do it?

If it's practical, then consider standing on a chair, and have the camera in the portrait (vertical) position, assuming that this does not cut off any people on the side.  Then follow the other suggestions (Aperture mode, stopped down to maybe f/5.6, focusing in the middle of the group).  Take some shots without flash (you may need ISO1600 or 3200) and some with flash (ISO400 should be OK), some with flash pointing straight ahead and some with it bounced.  (Warn people that this will take a while.)

Bob