I would take a look at an interesting drywall product that is engineered to be sound absorbing. It has a polyester layer in the middle that cuts sound transmission dramatically. You can caulk ceilings and floors if you want to get crazy ... with acoustic caulk.
That appears to be a re-marketing of the age-old classic Homasote 440. Very low mass - low isolation. There may be a chewey damping layer in between, but damping two lightweight boards is minimally impactful.
I strongly suggest looking at double 5/8" Type X drywall. There's no lightweight soundproofing.