Thanks Randy,
Yeah, I realised it was going to be impossible to pull the rubber between floor and joists. And it seems the problem is deflection - those joists are really singing a deep bass tone. They vibrate like crazy.
So:
Blocking between the joists (maybe better than cross-hatching??).
Isolated ceiling.
Screw down the floor from upstairs.
Is that going to be enough?
What I mean is really, given what you see in that picture, do you think we will get a result from doing all that without pulling up the upstairs floor and laying a subfloor?
Would it be a lot, lot, lot better with a subfloor?