Are those fancy sound canceling headphones an option?
When we remodeled we removed a few steel posts to free up space for the rec room. The contractor put in a massive laminate beam set on 6x6 posts with their own concrete piers. The ceiling was insulated. The floor above is 70 year old tongue+groove oak sitting on top of 3/4" thick slats running diagonally to the floor joists. When you are in the basement rec room you can't hear jack squat that is going on in the kitchen/den above you. Not quite as extreme as frenchyd, but not far off.
I suggest rugs for the upstairs and noise canceling headphones.
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