During our remodel when we removed the drywall from the dropped ceiling, there was no insulation between the 2x4s used to create the ceiling joists. Above this drop ceiling are the 2x8 floor joists of the story above. The space between the floor joists are insulated with kraft paper facing down toward the room being re-modeled.
It seems that it would be beneficial to fill the space between the 2x4s of the drop ceiling to eliminate the air space by adding insulation. Can new insulation be installed with kraft paper vapor barrier facing toward the living space just as the current insulation is oriented, or does un-faced insulation need to be used?
Any other suggestions?

Normally don't insulate between heated areas. Insulation between heated areas usually for sound proofing/deadening. Use insulation without vapor barrier.

Good luck

Chuck