Actually, you are forgetting the most important part that has more to do with tone quality and that is the actual stricking object, the felt on the hammer. That has more to do with sound quality than anything else. You sort of glossed over it but new pianos usually have a nicer overall tone than used ones because the felt/wool compresses after lots of use.Part of piano maintenance is voicing which the techy does to even out the tone or to voice it to the proper voice level. I need a proper voicing but would rather do it myself.My piano was "harsh" because the hammers were compressed at the point of impact. But I softened it a bit using some very ghetto, but effective, methods. It now has a nicer, more gentle tone to it and it sounds nicer.
I don't know. I don't think a "harsh" piano can every be "sweet" no matter how you play it. I've never played on a piano that had multiple tone qualities. All of them had just one quality no matter how I pressed the keys whether it be fast or slow.