Sure, in some cases, I have used multiple sheets of drywall too. It all adds to sound deadening, and, fairly cheap and easy to install. In your case, some combo of drywall/acoustical tile and regular insulation should do the trick.

good luck!

For least expensive and to lose the least headroom, I'd recommend you take a look into using a resilient channel.

Screw the RC to the ceiling joists, then screw the drywall to the RC. It decouples the drywall from the structural framing.

If you can add a second layer of drywall, that'd help too.

The idea of adding cut up ceiling tile to the acoustical insulation within the framing bay probably won't help as much as actually decoupling the framing from the finish surfaces of the two rooms.

Mongoct - obviously you are knowledgeable about this, and your advice is of course the correct method to properly address this issue.

Just a heads-up though, this OP has posted numerous questions regarding his "basement home theater project" without ever replying to, or simply acknowledging anybody.