You know, when you said something about the Piano voice sounding "not quite right," I had assumed you meant the quality of the wave samples, or something about the timbre that needed tweaking. But as I was playing with the LPF Cutoff/Resonance settings on the Grand Piano voice, I was noticing how the chords had a bit of dissonant interaction between the frequencies of the notes, which seemed to be accentuated by certain LPF settings. And while I was posting my observations, I took another look at the thread's title-- "Chord Piano Styles"-- which made me think that perhaps you really meant the consonance or dissonance of the various note intervals.
Unfortunately, I'm afraid the Scale Tuning feature is going to be a bit of a trade-off, since the whole reason Equal Temperament tuning was adopted in the first place is to ensure that the different intervals are always consistent no matter what keys they're played in, not to mention getting rid of ear-jarring wolf intervals. Of course, it also means perfect fifths and other intervals no longer have pleasing harmonic relationships between the notes! So you can get more consonant intervals by changing the note tunings of the scale, but you also have to choose a specific "base" key for the scale when you tune.
Another thing to keep in mind with regard to the Scale Tuning feature is that the adjustments are in terms of cents, whereas the difference between the tunings of a perfect fifth in Equal Temperament versus Just Intonation is an oddball irrational value. Thus, it probably won't be possible to get an exact 3:2, or 4:3, or 5:4, etc., harmonic relationship between the notes, so you'll have to settle for whichever whole-cent offsets are closest to the perfect harmonic ratios.