You can very slightly improve transmission to the upstairs with a layer of MDF/etc. glued to the undersides. Just understand that the joists which are connected to the floor above are still exposed and will still transmit sound very well.
As for the mineral wool - save your money. With a cavity the depth of a floor joist, you can use standard insulation and it will work just fine in that thickness. Also, don't do the entire ceiling or the room will be way way too dead in the upper mids and highs. Do only around the perimeter and potentially over your head.
If you need to do more, use faced insulation that will help reflect some of the high frequencies.
Bryan Pape
Lead Acoustic Designer - GIK Acoustics
As for the mineral wool - save your money. With a cavity the depth of a floor joist, you can use standard insulation and it will work just fine in that thickness. Also, don't do the entire ceiling or the room will be way way too dead in the upper mids and highs. Do only around the perimeter and potentially over your head.
If you need to do more, use faced insulation that will help reflect some of the high frequencies.
Bryan Pape
Lead Acoustic Designer - GIK Acoustics