We are eliminating the old dropped drywall ceiling in the kitchen. The ceiling framing is 2x12s (supporting the 2nd floor) and 2x6s that had created the drop ceiling originally. The photo shows how the 2x6 rests (not nailed) on edge under the 2x12 -- but the 2x6 is framing is NOT structural. The 2x6 will stay but the new drywall will cover it.
My problem (see photo) is the Romex which was fed through the 2x6. It has to be re-routed upward into the 2x12 to allow for the new (higher) drywall celing. The wire runs completely across the new recessed area in the ceiling and there is no slack in it. The garage is on the other side of that wall and the Romex plus other wires seem to be bundled and dropped into the main service panel at the far end.