Cheapest way i can think of: buy a celling tile case and a tacker, cut the celing tile un a T shape and tack them on both side between each of the truss. No need to put anything between them. That’ll cost around 100$.

Forget the drywall celling for a while you should at least replace all the stuff that’s gonna be stuck in there for peace of mind. Then you can think about it.

You should get that celling tile for the whole celling asap this will help with the soundproofing of the first level. Consider extra soundproofing after this.