What could be causing a dripping noise in the ceiling?
You sure it's a drip and not just the ducts popping from expansion and contraction? Post a video with sound. Generally one doesn't start opening walls until a leak is confirmed. Apply presser to the register when it's making this noise, if it stops it is just your ducts popping. To high of a velocity across the coil could carry water into the ductwork, but this probably isn't your problem if the offending register is any great amount of distance from the unit.