Brian,
Probably the best solution (although not the cheapest) is to install a suspended ceiling, dropping it no more than 6 inches below the joists and piping that is shown in your second picture. You'll need to frame in around the HVAC duct runs where they are lower than the drop ceiling would be. You'll need to lower the smoke detector, too. If done with T-track hung on wires, it should be a good sound barrier when the acoustic tiles are installed. If you lay fiberglass batts on top of the tiles, you'll have a very good acoustic barrier. I plan a suspended ceiling when I can afford one, but I do have 2' x 4' drop-in 4-bulb T8 fluorescent fixtures (troffers from BORG for about $45 each, made for suspended ceilings) hung on chains. I have 6" fiberglass batts in my shop ceiling joists and it cuts the sound by 90%, even though they are exposed like yours.
The second method is to attach Z-strips -- also known as resilient channel -- to the bottom of the joists and then attach a ceiling to them. The ceiling can be drywall on 2 x 2 furring strips attached to the Z-strips of an acoustical tile ceiling. The Z-strips isolate any vibrations through the new ceiling to the floor above. Make sure you do not have any vibration-carrying items tied to the floor joists above as they will make the floor vibrate and carry sound through.
Hope this helps...