I think that a large quilt will help in the same way that curtains help. I removed the carpeting in my living/dining room once and had the hardwood floors underneath refinished, and it took me weeks to get used to the new sounds in the house - everything echoed. I realize the area of the carpet is much larger than a quilt, but every bit helps.
Maybe the person could put up something really good for soundproofing and have it hidden behind the quilt.
Sorry, I have no advice on the best kind of batting. Probably whatever is the most dense.