Framing and Sub-Flooring - Homasote SoundProofing

Hello again! I'm killing myself trying to figure out the best and most cost effective way to sound proof our condo floor. I am very suspicious of various products available out there, which make ridiculous claims and cost $3+ a sqft. Bylaws require carpets, but we're hoping by adding soundproofing and area rugs, we can have hardwood floor.

Basically, I want to reduce as much Sound and Impact transmission as my budget will allow. Right now, I'm down to plank subflooring, and I was planning to put down 1/2" TG plywood underlay, with 440 SoundBarrier on top, and the hardwood floor (or laminate) on top. However aren't the cleats used to hold down the floor still going to transmit most of the Impact noise throught the SoundBarrier?

With that being said, if anyone out there has any suggestions or experience with what will work best, or which setup is better, please do share them! I'm thinking of possibly doing a floated or glue down assembly of the engineered or laminate hardwood on top of what I described. But perhaps there is some other readily available and not over priced sound proofing material that will do a better job for the price. The thin felt pad available at the flooring store seems more like an overpriced joke than a sound barrier.

Thanks for reading and any suggestions!