The best approach when dealing with a gap of this size (e.g.
2 inches), is to buy sufficient enough drywall so that you can either (1)
install a 2 inch wide strip of drywall at one end of the ceiling or (2) cut
two lengths of drywall 4ft 1 inch in length. Personally I would recommend
option number (2) as the cost of sheetrock is relatively inexpensive and you
will enhance your ability to get a clean looking ceiling.
When you start installing thin narrow filler drywall strips, the
drywall begins to break down when you nail/screw it. When securing the narrow
strips the drywall may crumble or bulge around the nail/screw, making it more
difficult to tape and mud.