You mentioned the possibility of installing a floating floor in the upstairs, and that’s a very good option. These rest in place on top of most types of old floor surfaces, and don’t require the use of fasteners to hold them down. Laminate floors are the most common floating floor option, and you’ll find leading manufacturers offer a variety of underlay products, some for situations just like yours.
Other sound-reducing underlays are also emerging for use under other flooring choices. One that I’ve looked at closely is called Regupol-QT. It’s made of reclaimed rubber, and has been proven effective at stopping both airborne sound and impact noises from people walking and running. This product is available from Wilrep (905-625-8944).
It’s also possible to install a layer of extruded polystyrene foam (those blue or pink sheets you see on building sites) on top of the existing floor. A layer of 1/2-inch plywood on top of that gets screwed down into the floor framing before your new floor goes down. One reason the foam-and-plywood option works so well is the differences in density that occur through the material. Changes in density thwart sound transmission well.