The 2" of extruded polystyrene is not too different from the same material used under airport runways. Don't worry that your kids will be bouncing off the ceiling. Two alternative systems without insulation areDri-Core and Delta FL; both types have competitors with similar systems. The concrete screws are not "dug" into the concrete. They're drilled in. The depth of embedment varies with the diameter of the screws you're using. Follow the instructions on the package.

"One of the principles commonly misunderstood about sound transfer in a floor is that sound energy is transfered by more than one method and that all methods must be addressed for reasonable success. A completely separate ceiling system interrupts structural transfer but not the indirect transfer through the air space between the ceiling and the floor in both directions." The problem with noise through floors is that it is low frequency impact noise that IS transmitted. It is the hardest thing to stop. Sound insulation works well for filling the volume and stopping noise that is NOT conducted. If you tie to the surface that can conduct noise you end up needing isolated mass to try and limit transmission. The mass of the light steel framing and drywall are often not adequate. you can improve the performance by adding more mass to the drywall (thicker or more layers) but you have to play that against the 'stiffness' of the fastening means. More weight requires stiffer fastening, increasing the sound transmitted. Concrete floors work very well since they are so massive it is very hard for anything much to be conducted, and fiberglass sound insulation takes care of the rest of the problem. If you are in a framed structure (wood or steel joists) the most effective method that works every time is a false ceiling with separate joists (sometimes you can put them between the existing joists to get back some headroom) and fiberglass sound insulation. All the various isolation fasteners end up having problems based on the suspended mass and their relative stiffness.

Read everything you possibly can at Building Science about insulation and vented vs unvented attics. Here’s a start. https://www.buildingscience.com/documents/digests/bsd-102-understanding-attic-ventilation

You need to find a blown insulation with ACOUSTIC ratings. And there's the rub. Most homeowners hear the word "insulation" and think thermal. But when they want acoustic insulation, they also think "insulation". And when the speak to THERMAL insulating professionals the word "insulation" gets misinterpreted (by both parties). The DENSITY of the material and the VARIABILITY of the particle sizes will dictate how much acoustic insulation you will get. Here's an example: A friend of mine used the acoustic calking in her basement ceiling. She then stuffed the ceiling joists with a SINGLE layer of Roxul Safe N Sound - even though I SPECIFICALLY stated she needed to DOUBLE stuff. Then installed acoustic channels and then regular drywall. She wishes she had listened to me about the double stuffing of Roxul. I didn't take the time to listen to a sales guy talking about the actual numbers for cellulose insulation, but here's a link that might help. https://deenergyconservers.ca/sound-properties-acoustical.htm I'm always suspicious of lab tests because the manufacturers will pay HUGE amounts of money to FILL the testing lab with thens of THOUSANDS of dollars worth of building materials so they can get 'massive' numbers from 4inches of blown insulation. They then publish the numbers for the ENTIRE assembly (could be 3-4 FEET worth of material) and claim it is the rating for their 4" worth of insulation. It's a trick I REALLY HATE. That's why I only look at Delta IIC ratings.