Soundproofing a floor: How about cement backer board w/ Green Glue and mass-loaded vinyl?
The reason the floor materials aren't as effective is because this problem is best solved with an air-gap and a flexible connection spanning that air-gap. But you have a hard time supporting a floor with that air-gap. Therefore, solving this problem via the ceiling below this floor is better, using resilient or sound attenuation channel there.

That said, on your floor, carpeting over Homasote, QuietWood, or some other material will be as good as you'll get on the floor. Since I don't have experience with MLV or GG, I'll defer to others on that. However, the cement backer board seems like the weak link here since that will transmit sound rather than absorb it.