What’s the reason for the drop ceiling as opposed to drywall. Is there pipes/or anything hanging below floor joists? If there isn’t then I would remove drop ceiling and drywall it. If there is a few things below the joists you still may be able to do drywall just have to frame around lower obstacles. Doesn’t look like that big of a room so it would be fairly easy IMO. Could even put rockwool insulation batts in the ceiling cavity to greatly reduce sound to the upstairs.