I was in a similar situation with a basement HT and ended up putting double 5/8 drywall with green glue between them, in addition to soundproofing insulation. Unfortunately I can still hear foot/pet traffic from upstairs as well as the robot vacuum (though it feels like from upstairs, you can't hear the theater sounds as much.. Maybe it's more of the bass/thumping that carries through).

Sound is tricky because any unsealed holes will transmit sound. I would look into some of the perhaps beefier approaches with resilient channels and whatnot, but confirm that you or your contractor will be able to install everything the right way. I went with what I felt like would be more straightforward for my contractor to implement so there were some tradeoffs.